Finite-dimensional algebra over a field

Definition

A finite-dimensional algebra over a field is a commutative unital ring that contains a subfield, such that the ring is finite-dimensional, when viewed as a vector space over the field. The dimension here is not to be confused with the Krull dimension, which is always zero for such algebras.

Relation with other properties

Weaker properties

• Zero-dimensional ring
• Jacobson ring