Definition:Underlying Ring of Associative Algebra

Definition

Let $R$ be a commutative ring.

Let $\struct {A, *}$ be an associative algebra over $R$.

Let $A = \struct {M, +, \circ}$ be the underlying module of $\struct {A, *}$.

The underlying ring of $\struct {A, *}$ is the ring $\struct {A, +, *}$.

Also see

• Underlying Ring of Associative Algebra is Ring
• Definition:Underlying Ringoid of Algebra

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