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Mirrors > Home > MPE Home > Th. List > df-lidl | Structured version Visualization version GIF version |
Description: Define the class of left ideals of a given ring. An ideal is a submodule of the ring viewed as a module over itself. For the usual textbook definition of a (left) ideal of a ring to be a subgroup of the additive group of the ring which is closed under left-multiplication by elements of the full ring, see dflidl2 20842. (Contributed by Stefan O'Rear, 31-Mar-2015.) |
Ref | Expression |
---|---|
df-lidl | ⊢ LIdeal = (LSubSp ∘ ringLMod) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | clidl 20782 | . 2 class LIdeal | |
2 | clss 20541 | . . 3 class LSubSp | |
3 | crglmod 20781 | . . 3 class ringLMod | |
4 | 2, 3 | ccom 5680 | . 2 class (LSubSp ∘ ringLMod) |
5 | 1, 4 | wceq 1541 | 1 wff LIdeal = (LSubSp ∘ ringLMod) |
Colors of variables: wff setvar class |
This definition is referenced by: lidlval 20813 |
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