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Mirrors > Home > MPE Home > Th. List > df-lvec | Structured version Visualization version Unicode version |
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.) |
Ref | Expression |
---|---|
df-lvec |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | clvec 18403 |
. 2
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2 | vf |
. . . . . 6
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3 | 2 | cv 1451 |
. . . . 5
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4 | csca 15271 |
. . . . 5
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5 | 3, 4 | cfv 5589 |
. . . 4
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6 | cdr 18053 |
. . . 4
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7 | 5, 6 | wcel 1904 |
. . 3
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8 | clmod 18169 |
. . 3
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9 | 7, 2, 8 | crab 2760 |
. 2
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10 | 1, 9 | wceq 1452 |
1
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Colors of variables: wff setvar class |
This definition is referenced by: islvec 18405 bj-vecssmod 31768 |
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