Let R be a ring and M a left R-module. Show that, for any idempotent e ER End(M) We have ker(e) = im(Id-e)

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 15E: 15. In a commutative ring of characteristic 2, prove that the idempotent elements form a subring of...
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Let R be a ring and M a left R-module. Show that, for any idempotent e
ER End(M) We have ker(e) = im(Id-e)
Transcribed Image Text:Let R be a ring and M a left R-module. Show that, for any idempotent e ER End(M) We have ker(e) = im(Id-e)
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