In mathematics, an algebra over a field is a vector space equipped with a bilinear product. Wikipedia

Vector space equipped with a bilinear product Wikidata

A vector space (over some field) with an additional binary operation, a vector-valued product between vectors, which is bilinear over vector addition and scalar multiplication. (N.B.: such bilinearity implies distributivity of the vector multiplication with respect to the vector addition, which means that such a vector space is also a ring.). Wiktionary