Commutative unital ring

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This article is about a basic definition in commutative algebra. View a complete list of basic definitions in commutative algebra

Definition

A commutative unital ring is a set R endowed with two binary operations + and *, and constants 0 and 1 such that:

  • R is an Abelian group under +, with identity element 0
  • R is an Abelian monoid under *, with identity element 1
  • Left and right distributivity laws hold:

a * (b + c) = (a * b) + (a * c)

and:

(a + b) * c = (a * c) + (b * c)