-s] Assume that * is an operation on S with identity element e, and thatx * (y * z) = (x * z) * yfor all x, y, z E S. Prove that is commutative and associative.

A operation " o " on S is said to be commutative if x o y = y o x for all x and y in S And…

Answered: s] Assume that is an operation on S…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.2: Integral Domains And Fields

Problem 17E: If e is the unity in an integral domain D, prove that (e)a=a for all aD. [Type here][Type here]

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s] Assume that is an operation on S with identity element e, and that x * (y * 2) = (x * z2) * y for all a, y, z E S. Prove that * is commutative and associative.