Exercise 14.4. Let R be a ring, andZ(R) = {a Є R | ab = ba, \b € R}For every nЄN, show thatZ(Mn(R))=- {( - ) \ - - x m}a Z(R)

Solution:To prove that Z(R) is a subring of R, we need to show that it satisfies: Step1. Non-empty:…

Answered: Exercise 14.4. Let R be a ring, and…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.3: Divisibility

Problem 30E: Let be as described in the proof of Theorem. Give a specific example of a positive element of .

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Exercise 14.4. Let R be a ring, and Z(R) = {a Є R | ab = ba, \b € R} For every nЄN, show that Z(Mn(R)) = - {( - ) \ - - x m} a Z(R)