Like unit rings, properties of these mathematic objects include commutativity, associativity, the existence of unique additive and multiplicative identities, and a unique additive inverse for every element.
Like unit rings, properties of these mathematic objects include commutativity, associativity, the existence of unique additive and multiplicative identities, and a unique additive inverse for every element. Finite dimensional ones have a natural isomorphism with their double duals, are free, injective, projective, and flat as modules, and are isomorphic to a finite Cartesian product of fields. Zorn's Lemma can be invoked to show that a set of elements exists in any of them such that any element can be written uniquely as a linear combination of finitely many elements in that set. FTP, name these objects which are modules over a field, of which an example is three dimensional real space.
Like unit rings, properties of these mathematic objects include commutativity, associativity, the existence of unique additive and multiplicative identities, and a unique additive inverse for every element.
vector space