noun
: a set representing a generalization of a system of vectors and consisting of elements which comprise a commutative group under addition, each of which is left unchanged under multiplication by the multiplicative identity of a field, and for which multiplication under the multiplicative operation of the field is commutative, closed, distributive such that both c(A + B) = cA + cB and (c + d)A = cA + dA , and associative such that (cd)A = c(dA) where A, B are elements of the set and c, d are elements of the field