(a) If A and Bare R modules, then the set Hom R (A,B) of all R module homomorphisms A B is an abelian group with g given on a A by( g)(a) f(a) g(a) B The identity element is the zero map (b) Hom R (A,A) is a ring with identity, where multiplication is composition of functions Hom R (A,A) is called ...

a The set HomRAB is an abelian group under pointwise addition since the sum of two Rmodule homomorph ...

(a) If A and Bare R-modules, then the set Hom R (A,B) of all R-module homomorphisms A...

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(a) If A and Bare R-modules, then the set Hom_R(A,B) of all R-module homomorphisms A → B is an abelian group with ∫ + g given on a ϵ A by(∫+ g)(a) = f(a) + g(a) ϵ B. The identity element is the zero map.

(b) Hom_R(A,A) is a ring with identity, where multiplication is composition of functions. Hom_R(A,A) is called the endomorphism ring of A.

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Algebra Graduate Texts In Mathematics 73

ISBN: 9780387905181

8th Edition

Authors: Thomas W. Hungerford

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Question Posted: Apr 15, 2023 03:04 AM

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(a) If A and Bare R-modules, then the set Hom R (A,B) of all R-module homomorphisms A...

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f(a) (a e A,fe HomR(A,A)).

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a The set HomRAB is an abelian group under pointwise addition since the sum of two Rmodule homomorph...View the full answer

Algebra Graduate Texts In Mathematics 73

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