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 häs no non-zeró nilpotent elements. a is nilpotent and so axa = a. (ii) axa (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 häs no non-zeró nilpotent elements. a is nilpotent and so axa = a. (ii) axa (iii) ax and xa are idempotents.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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