Category-3AProperties of commutative unital rings
type: Ontology
creation date: 2026-03-15T01:43:18+00:00
imports: http://semantic-mediawiki.org/swivt/1.0

Properties of commutative unital rings
type: Class
page: https://commalg.subwiki.org/wiki/Category-3AProperties_of_commutative_unital_rings
wiki namespace: 14
wiki page content language: en
wiki page modification date: 2008-05-12T18:06:26Z
modification date#aux: 2454599.2544676
wiki page sort key: Properties of commutative unital rings
subclass of: Category:Properties
subclass of: Category:Monster categories

Ring satisfying ACCP
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Ring_satisfying_ACCP
wiki namespace: 0
wiki page content language: en
wiki page sort key: Ring satisfying ACCP

Adequate domain
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Adequate_domain
wiki namespace: 0
wiki page content language: en
wiki page sort key: Adequate domain

Affine domain
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Affine_domain
wiki namespace: 0
wiki page content language: en
wiki page sort key: Affine domain

Artinian ring
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Artinian_ring
wiki namespace: 0
wiki page content language: en
wiki page sort key: Artinian ring

Bezout domain
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Bezout_domain
wiki namespace: 0
wiki page content language: en
wiki page sort key: Bezout domain

Gcd domain
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Gcd_domain
wiki namespace: 0
wiki page content language: en
wiki page sort key: Gcd domain

Bezout ring
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Bezout_ring
wiki namespace: 0
wiki page content language: en
wiki page sort key: Bezout ring

Euclidean domain
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Euclidean_domain
wiki namespace: 0
wiki page content language: en
wiki page sort key: Euclidean domain

Principal ideal domain
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Principal_ideal_domain
wiki namespace: 0
wiki page content language: en
wiki page sort key: Principal ideal domain

Multi-stage Euclidean domain
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Multi-2Dstage_Euclidean_domain
wiki namespace: 0
wiki page content language: en
wiki page sort key: Multi-stage Euclidean domain

Catenary ring
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Catenary_ring
wiki namespace: 0
wiki page content language: en
wiki page sort key: Catenary ring

Noetherian ring
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Noetherian_ring
wiki namespace: 0
wiki page content language: en
wiki page sort key: Noetherian ring

Universally catenary ring
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Universally_catenary_ring
wiki namespace: 0
wiki page content language: en
wiki page sort key: Universally catenary ring

Cohen-Macaulay ring
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Cohen-2DMacaulay_ring
wiki namespace: 0
wiki page content language: en
wiki page sort key: Cohen-Macaulay ring

Local Cohen-Macaulay ring
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Local_Cohen-2DMacaulay_ring
wiki namespace: 0
wiki page content language: en
wiki page sort key: Local Cohen-Macaulay ring

Regular local ring
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Regular_local_ring
wiki namespace: 0
wiki page content language: en
wiki page sort key: Regular local ring

Regular ring
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Regular_ring
wiki namespace: 0
wiki page content language: en
wiki page sort key: Regular ring

Dedekind domain
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Dedekind_domain
wiki namespace: 0
wiki page content language: en
wiki page sort key: Dedekind domain

Finite-dimensional algebra over a field
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Finite-2Ddimensional_algebra_over_a_field
wiki namespace: 0
wiki page content language: en
wiki page sort key: Finite-dimensional algebra over a field

Coherent ring
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Coherent_ring
wiki namespace: 0
wiki page content language: en
wiki page sort key: Coherent ring

Complete intersection
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Complete_intersection
wiki namespace: 0
wiki page content language: en
wiki page sort key: Complete intersection

Complete local ring
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Complete_local_ring
wiki namespace: 0
wiki page content language: en
wiki page sort key: Complete local ring

Normal ring
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Normal_ring
wiki namespace: 0
wiki page content language: en
wiki page sort key: Normal ring

Normal domain
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Normal_domain
wiki namespace: 0
wiki page content language: en
wiki page sort key: Normal domain

One-dimensional ring
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/One-2Ddimensional_ring
wiki namespace: 0
wiki page content language: en
wiki page sort key: One-dimensional ring

Noetherian domain
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Noetherian_domain
wiki namespace: 0
wiki page content language: en
wiki page sort key: Noetherian domain

One-dimensional domain
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/One-2Ddimensional_domain
wiki namespace: 0
wiki page content language: en
wiki page sort key: One-dimensional domain

Noetherian normal domain
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Noetherian_normal_domain
wiki namespace: 0
wiki page content language: en
wiki page sort key: Noetherian normal domain

Ring of integers in a number field
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Ring_of_integers_in_a_number_field
wiki namespace: 0
wiki page content language: en
wiki page sort key: Ring of integers in a number field

Integral domain
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Integral_domain
wiki namespace: 0
wiki page content language: en
wiki page sort key: Integral domain

Elementary divisor domain
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Elementary_divisor_domain
wiki namespace: 0
wiki page content language: en
wiki page sort key: Elementary divisor domain

Elementary divisor ring
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Elementary_divisor_ring
wiki namespace: 0
wiki page content language: en
wiki page sort key: Elementary divisor ring

Equicharacteristic ring
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Equicharacteristic_ring
wiki namespace: 0
wiki page content language: en
wiki page sort key: Equicharacteristic ring

Equidimensional catenary ring
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Equidimensional_catenary_ring
wiki namespace: 0
wiki page content language: en
wiki page sort key: Equidimensional catenary ring

Equidimensional ring
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Equidimensional_ring
wiki namespace: 0
wiki page content language: en
wiki page sort key: Equidimensional ring

Local Noetherian domain
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Local_Noetherian_domain
wiki namespace: 0
wiki page content language: en
wiki page sort key: Local Noetherian domain

Unique factorization domain
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Unique_factorization_domain
wiki namespace: 0
wiki page content language: en
wiki page sort key: Unique factorization domain

Uniquely Euclidean domain
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Uniquely_Euclidean_domain
wiki namespace: 0
wiki page content language: en
wiki page sort key: Uniquely Euclidean domain

Principal ideal ring
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Principal_ideal_ring
wiki namespace: 0
wiki page content language: en
wiki page sort key: Principal ideal ring

Field
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Field
wiki namespace: 0
wiki page content language: en
wiki page sort key: Field

Finite-dimensional Noetherian ring
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Finite-2Ddimensional_Noetherian_ring
wiki namespace: 0
wiki page content language: en
wiki page sort key: Finite-dimensional Noetherian ring

Finite-dimensional ring
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Finite-2Ddimensional_ring
wiki namespace: 0
wiki page content language: en
wiki page sort key: Finite-dimensional ring

Finite ring
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Finite_ring
wiki namespace: 0
wiki page content language: en
wiki page sort key: Finite ring

Henselian local ring
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Henselian_local_ring
wiki namespace: 0
wiki page content language: en
wiki page sort key: Henselian local ring

Hereditary ring
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Hereditary_ring
wiki namespace: 0
wiki page content language: en
wiki page sort key: Hereditary ring

Jacobson ring
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Jacobson_ring
wiki namespace: 0
wiki page content language: en
wiki page sort key: Jacobson ring

Irreducible ring
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Irreducible_ring
wiki namespace: 0
wiki page content language: en
wiki page sort key: Irreducible ring

Zero-dimensional ring
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Zero-2Ddimensional_ring
wiki namespace: 0
wiki page content language: en
wiki page sort key: Zero-dimensional ring

Japanese ring
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Japanese_ring
wiki namespace: 0
wiki page content language: en
wiki page sort key: Japanese ring

Noetherian local ring
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Noetherian_local_ring
wiki namespace: 0
wiki page content language: en
wiki page sort key: Noetherian local ring

Local domain
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Local_domain
wiki namespace: 0
wiki page content language: en
wiki page sort key: Local domain

Local ring
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Local_ring
wiki namespace: 0
wiki page content language: en
wiki page sort key: Local ring

Locally a complete intersection
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Locally_a_complete_intersection
wiki namespace: 0
wiki page content language: en
wiki page sort key: Locally a complete intersection

Nagata ring
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Nagata_ring
wiki namespace: 0
wiki page content language: en
wiki page sort key: Nagata ring

Noetherian UFD
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Noetherian_UFD
wiki namespace: 0
wiki page content language: en
wiki page sort key: Noetherian UFD

Primary ring
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Primary_ring
wiki namespace: 0
wiki page content language: en
wiki page sort key: Primary ring

Quasi-Frobenius ring
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Quasi-2DFrobenius_ring
wiki namespace: 0
wiki page content language: en
wiki page sort key: Quasi-Frobenius ring

Reduced ring
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Reduced_ring
wiki namespace: 0
wiki page content language: en
wiki page sort key: Reduced ring

Ring satisfying PIT
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Ring_satisfying_PIT
wiki namespace: 0
wiki page content language: en
wiki page sort key: Ring satisfying PIT

Ring where every prime contains a minimal prime
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Ring_where_every_prime_contains_a_minimal_prime
wiki namespace: 0
wiki page content language: en
wiki page sort key: Ring where every prime contains a minimal prime

Ring where every prime contains a minimal prime and having finitely many minimal primes
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Ring_where_every_prime_contains_a_minimal_prime_and_having_finitely_many_minimal_primes
wiki namespace: 0
wiki page content language: en
wiki page sort key: Ring where every prime contains a minimal prime and having finitely many minimal primes

Ring with equal Krull dimension and global dimension
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Ring_with_equal_Krull_dimension_and_global_dimension
wiki namespace: 0
wiki page content language: en
wiki page sort key: Ring with equal Krull dimension and global dimension

Semiprimitive ring
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Semiprimitive_ring
wiki namespace: 0
wiki page content language: en
wiki page sort key: Semiprimitive ring

S2-ring
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/S2-2Dring
wiki namespace: 0
wiki page content language: en
wiki page sort key: S2-ring

Semihereditary ring
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Semihereditary_ring
wiki namespace: 0
wiki page content language: en
wiki page sort key: Semihereditary ring

Semisimple Artinian ring
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Semisimple_Artinian_ring
wiki namespace: 0
wiki page content language: en
wiki page sort key: Semisimple Artinian ring

Integral domain in which every irreducible is prime
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Integral_domain_in_which_every_irreducible_is_prime
wiki namespace: 0
wiki page content language: en
wiki page sort key: Integral domain in which every irreducible is prime

Integral domain in which any two irreducible factorizations are equal upto ordering and associates
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Integral_domain_in_which_any_two_irreducible_factorizations_are_equal_upto_ordering_and_associates
wiki namespace: 0
wiki page content language: en
wiki page sort key: Integral domain in which any two irreducible factorizations are equal upto ordering and associates

Ring over which nonzero polynomials define nonzero functions
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Ring_over_which_nonzero_polynomials_define_nonzero_functions
wiki namespace: 0
wiki page content language: en
wiki page sort key: Ring over which nonzero polynomials define nonzero functions

Ring over which every monic polynomial has finitely many roots
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Ring_over_which_every_monic_polynomial_has_finitely_many_roots
wiki namespace: 0
wiki page content language: en
wiki page sort key: Ring over which every monic polynomial has finitely many roots

Ring over which every nonzero polynomial has finitely many roots
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Ring_over_which_every_nonzero_polynomial_has_finitely_many_roots
wiki namespace: 0
wiki page content language: en
wiki page sort key: Ring over which every nonzero polynomial has finitely many roots

Interpolation domain
type: Subject
type: Properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Interpolation_domain
wiki namespace: 0
wiki page content language: en
wiki page sort key: Interpolation domain

Properties of integral domains
type: Class
page: https://commalg.subwiki.org/wiki/Category-3AProperties_of_integral_domains
wiki namespace: 14
wiki page content language: en
wiki page sort key: Properties of integral domains
subclass of: Properties of commutative unital rings

Properties of local rings
type: Class
page: https://commalg.subwiki.org/wiki/Category-3AProperties_of_local_rings
wiki namespace: 14
wiki page content language: en
wiki page sort key: Properties of local rings
subclass of: Properties of commutative unital rings

Polynomial-closed properties of commutative unital rings
type: Class
page: https://commalg.subwiki.org/wiki/Category-3APolynomial-2Dclosed_properties_of_commutative_unital_rings
wiki namespace: 14
wiki page content language: en
wiki page sort key: Polynomial-closed properties of commutative unital rings
subclass of: Properties of commutative unital rings

Spectrum-determined properties of commutative unital rings
type: Class
page: https://commalg.subwiki.org/wiki/Category-3ASpectrum-2Ddetermined_properties_of_commutative_unital_rings
wiki namespace: 14
wiki page content language: en
wiki page sort key: Spectrum-determined properties of commutative unital rings
subclass of: Properties of commutative unital rings

Localization-closed properties of commutative unital rings
type: Class
page: https://commalg.subwiki.org/wiki/Category-3ALocalization-2Dclosed_properties_of_commutative_unital_rings
wiki namespace: 14
wiki page content language: en
wiki page sort key: Localization-closed properties of commutative unital rings
subclass of: Properties of commutative unital rings

Completion-closed properties of commutative unital rings
type: Class
page: https://commalg.subwiki.org/wiki/Category-3ACompletion-2Dclosed_properties_of_commutative_unital_rings
wiki namespace: 14
wiki page content language: en
wiki page sort key: Completion-closed properties of commutative unital rings
subclass of: Properties of commutative unital rings

Strongly local properties of commutative unital rings
type: Class
page: https://commalg.subwiki.org/wiki/Category-3AStrongly_local_properties_of_commutative_unital_rings
wiki namespace: 14
wiki page content language: en
wiki page sort key: Strongly local properties of commutative unital rings
subclass of: Properties of commutative unital rings

INST
type: DatatypeProperty
page: https://commalg.subwiki.org/wiki/Property-3A_INST
wiki namespace: 132
wiki page content language: en
wiki page sort key: INST

Subcategory of
type: ObjectProperty
page: https://commalg.subwiki.org/wiki/Property-3ASubcategory_of
wiki namespace: 132
wiki page content language: en
wiki page sort key: Subcategory of