Question

Describe the endomorphism ring . Is it commutative? Justify your answer.​

Answer 1

Step-by-step explanation:

In abstract algebra, the endomorphisms of an abelian group X form a ring. This ring is called the endomorphism ring X, denoted by End(X); the set of all homomorphisms of X into itself. Addition of endomorphisms arises naturally in a pointwise manner and multiplication via endomorphism composition. Using these operations, the set of endomorphisms of an abelian group forms a (unital) ring, with the zero map {\textstyle 0:x\mapsto 0}{\textstyle 0:x\mapsto 0} as additive identity and the identity map {\textstyle 1:x\mapsto x}{\textstyle 1:x\mapsto x} as multiplicative identity.

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Answer 2

Step-by-step explanation:

endomphrism ringshave additive and multiplicative identies respectively zero map is identify mapendomorphism rings are associtive but typically non communicative if a moudle it's simpleits endophism ring is a division ring