Ring of Endomorphisms and Modules over a Ring

Summary We formalize in the Mizar system [3], [4] some basic properties on left module over a ring such as constructing via of endomorphism an abelian group and set all homomorphisms modules form [1] along with Ch. 2 set. 1 [2]. The formalized items are shown below list notations: M ab for Abelian suffix “ ” without is used ring. 1. denoted by End ( ). 2. A pair homomorphism R → ρ R\mathop \to \limits^\rho ) determines R -module, function AbGrLMod , ρ article. 3. functions from to N -module Func_Mod M, 4. Hom ), forms -module. 5. formal proof (¯ R, ≅ given, where ¯ denotes regular representation i.e. we regard itself 6. ′ ′) obtained removing scalar multiplication ρ′ currying . removal has been done forgettable functor defined AbGr