MathGloss

An algebra over a field $F$ is a vector space $U$ over $F$ with a bilinear binary operation $U\times U \to U$ that is not necessarily associative but that follows left and right distributivity.

One can loosen this definition and only require $F$ to be a commutative ring, but then you just get an algebra over a ring.

Wikidata ID: Q1000660

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