algebra over a field

Meaning

Noun

• 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.)

Related

Similar words

• algebra

Narrower meaning words

• associative algebra
• division algebra
• non-associative algebra

Broader meaning words

• ring
• vector space