Category:Definitions/Unital Associative Commutative Algebras

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This category contains definitions related to Unital Associative Commutative Algebras.
Related results can be found in Category: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.