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-zerò nilpotent elements. (ii) axa - a is nilpotent and so axa = a. (iii) ax and xa...

Prove (ii) and (iii)

Let R be a ring such that for each a e R there exists<br>XE R such that a'x = a. Prove the following :<br>(i) R häs no non-zerò nilpotent elements.<br>(ii) axa - a is nilpotent and so axa = a.<br>(iii) ax and xa are idempotents.<br>

Extracted text: 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-zerò nilpotent elements. (ii) axa - a is nilpotent and so axa = a. (iii) ax and xa are idempotents.

Jun 03, 2022

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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-zerò nilpotent elements. (ii) axa - a is nilpotent and so axa = a. (iii) ax and xa...

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