Category:Unital Associative Commutative Algebras

This category contains results about Unital Associative Commutative Algebras.
Definitions specific to this category can be found in Definitions/Unital Associative Commutative Algebras.

Let $R$ be a commutative ring with unity.

Definition 1

A unital associative commutative algebra over $R$ is an algebra $\struct {A, *}$ over $R$ that is unital, associative and commutative and whose underlying module is unitary.

Definition 2

A unital associative commutative algebra over $R$ is a ring under $A$, that is, an ordered pair $\struct {A, f}$ where:

$A$ is a commutative ring with unity

$f : R \to A$ is a unital ring homomorphism.