Answered: Let R be a ring with identity 1 and let…

Let R be a ring with identity 1 and let a be an element of R such that a2 = 1. Let S = { ara : r e R}. Prove that S is a subring of R that contains 1.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.1: Ideals And Quotient Rings

Problem 7E: Exercises Let be an ideal of a ring , and let be a subring of . Prove that is an ideal of

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Let R be a ring with identity 1 and let a be an element of R such that a² = 1. Let S = { ara : r e R}. Prove that S is a subring of R that contains 1.

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