Algebra (ring Theory) - Formal Definition

Formal Definition

Let R be a commutative ring. An R-algebra is an R-module A together with a binary operation

: A \times A\to A

called A-multiplication, which satisfies the following axiom:

  • Bilinearity:
for all scalars a, b in R and all elements x, y, z in A.

Read more about this topic:  Algebra (ring Theory)

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