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Definition df-lvec 18326
 Description: Define the class of all left vector spaces. A left vector space over a division ring is an Abelian group (vectors) together with a division ring (scalars) and a left scalar product connecting them. Some authors call this a "left module over a division ring", reserving "vector space" for those where the division ring multiplication is commutative i.e. a field. (Contributed by NM, 11-Nov-2013.)
Assertion
Ref Expression
df-lvec Scalar

Detailed syntax breakdown of Definition df-lvec
StepHypRef Expression
1 clvec 18325 . 2
2 vf . . . . . 6
32cv 1443 . . . . 5
4 csca 15193 . . . . 5 Scalar
53, 4cfv 5582 . . . 4 Scalar
6 cdr 17975 . . . 4
75, 6wcel 1887 . . 3 Scalar
8 clmod 18091 . . 3
97, 2, 8crab 2741 . 2 Scalar
101, 9wceq 1444 1 Scalar
 Colors of variables: wff setvar class This definition is referenced by:  islvec  18327  bj-vecssmod  31698
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