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Definition df-lvec 15856
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  |-  LVec  =  { f  e.  LMod  |  (Scalar `  f )  e.  DivRing }

Detailed syntax breakdown of Definition df-lvec
StepHypRef Expression
1 clvec 15855 . 2  class  LVec
2 vf . . . . . 6  set  f
32cv 1622 . . . . 5  class  f
4 csca 13211 . . . . 5  class Scalar
53, 4cfv 5255 . . . 4  class  (Scalar `  f )
6 cdr 15512 . . . 4  class  DivRing
75, 6wcel 1684 . . 3  wff  (Scalar `  f )  e.  DivRing
8 clmod 15627 . . 3  class  LMod
97, 2, 8crab 2547 . 2  class  { f  e.  LMod  |  (Scalar `  f )  e.  DivRing }
101, 9wceq 1623 1  wff  LVec  =  { f  e.  LMod  |  (Scalar `  f )  e.  DivRing }
Colors of variables: wff set class
This definition is referenced by:  islvec  15857
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