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Definition df-lvec 17360
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

Detailed syntax breakdown of Definition df-lvec
StepHypRef Expression
1 clvec 17359 . 2
2 vf . . . . . 6
32cv 1369 . . . . 5
4 csca 14400 . . . . 5
53, 4cfv 5537 . . . 4
6 cdr 17008 . . . 4
75, 6wcel 1758 . . 3
8 clmod 17124 . . 3
97, 2, 8crab 2804 . 2
101, 9wceq 1370 1
Colors of variables: wff setvar class
This definition is referenced by:  islvec  17361  bj-vecssmod  33430
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