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Elements Of Modern Algebra

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 22E: 22. Let be a ring with finite number of elements. Show that the characteristic of divides .

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

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