is its unity?(2) (A) Let R be a ring with the property that r² =r for all r e R. Show that(i) if a € R, then a+a = 0;(ii) if a, b € R, then ab = ba.

A ring is a triplet that is R,+,· where R is a set and uses two operations. It follows the following…

Answered: (2) (A) Let R be a ring with the…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.3: The Characteristic Of A Ring

Problem 5E

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(2) (A) Let R be a ring with the property that r² = r for all r € R. Show that (i) if a € R, then a + a=0; (ii) if a, b e R, then ab-ba.