Definition df-rgmod 14512

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 e. _V |-> ( (subringAlg ` w ) ` ( Base ` w ) ) )

Detailed syntax breakdown of Definition df-rgmod

Step	Hyp	Ref	Expression
1		crglmod 14510	. 2 class ringLMod
2		vw	. . 3 setvar w
3		cvv 2803	. . 3 class _V
4	2	cv 1397	. . . . 5 class w
5		cbs 13143	. . . . 5 class Base
6	4, 5	cfv 5333	. . . 4 class ( Base ` w )
7		csra 14509	. . . . 5 class subringAlg
8	4, 7	cfv 5333	. . . 4 class (subringAlg ` w )
9	6, 8	cfv 5333	. . 3 class ( (subringAlg ` w ) ` ( Base ` w ) )
10	2, 3, 9	cmpt 4155	. 2 class ( w e. _V |-> ( (subringAlg ` w ) ` ( Base ` w ) ) )
11	1, 10	wceq 1398	1 wff ringLMod = ( w e. _V |-> ( (subringAlg ` w ) ` ( Base ` w ) ) )

This definition is referenced by:  rlmfn  14529  rlmvalg  14530