An endomorphismof the group G is a homomorphism : G → G.Let End (A) be the set of all endomorphisms of the abelian groups A, that isEnd(A) := {y: A → Alya homomorphism}Define binary operations + and * on End(A) by(+)(a) = y(a) + (a) and(*)(a) = ((a))4for all a E A and p, & € End(A).Show that (End (A), +, *) is a ring.

Using the definition of ring set of endomorphism from A is form a Ring.

Answered: An endomorphism of the group G is a…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.7: Direct Sums (optional)

Problem 21E

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