algebra over a field

== English == === Noun === algebra over a field (plural algebras over a field) (algebra) An algebra over a ring such that the ring is in fact a field. As a module over a field, such an algebra is in particular a vector space. ==== Synonyms ==== algebra k-algebra ==== Hypernyms ==== ring vector space ==== Hyponyms ==== associative algebra division algebra non-associative algebra ==== Related terms ==== algebra over a ring