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Definition df-rgmod 19881
Description: Any ring can be regarded as a left algebra over itself. The function ringLMod associates with any ring the left algebra consisting in the ring itself regarded as a left algebra over itself. It has an inner product which is simply the ring product. (Contributed by Stefan O'Rear, 6-Dec-2014.)
Assertion
Ref Expression
df-rgmod ringLMod = (𝑤 ∈ V ↦ ((subringAlg ‘𝑤)‘(Base‘𝑤)))

Detailed syntax breakdown of Definition df-rgmod
StepHypRef Expression
1 crglmod 19877 . 2 class ringLMod
2 vw . . 3 setvar 𝑤
3 cvv 3500 . . 3 class V
42cv 1529 . . . . 5 class 𝑤
5 cbs 16478 . . . . 5 class Base
64, 5cfv 6354 . . . 4 class (Base‘𝑤)
7 csra 19876 . . . . 5 class subringAlg
84, 7cfv 6354 . . . 4 class (subringAlg ‘𝑤)
96, 8cfv 6354 . . 3 class ((subringAlg ‘𝑤)‘(Base‘𝑤))
102, 3, 9cmpt 5143 . 2 class (𝑤 ∈ V ↦ ((subringAlg ‘𝑤)‘(Base‘𝑤)))
111, 10wceq 1530 1 wff ringLMod = (𝑤 ∈ V ↦ ((subringAlg ‘𝑤)‘(Base‘𝑤)))
Colors of variables: wff setvar class
This definition is referenced by:  rlmfn  19898  rlmval  19899
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