Let R be a ring such that for each a e R there exists XE R such that a'x = a. Prove the following : (i) R has no non-zerò nilpotent elements. (ii) аха - a is nilpotent and so axa = a. (iii) ax and xa are idempotents.
Let R be a ring such that for each a e R there exists XE R such that a'x = a. Prove the following : (i) R has no non-zerò nilpotent elements. (ii) аха - a is nilpotent and so axa = a. (iii) ax and xa are idempotents.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter7: Real And Complex Numbers
Section7.2: Complex Numbers And Quaternions
Problem 51E: An element in a ring is idempotent if . Prove that a division ring must contain exactly two...
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