Let R be a ring. Call an element a = R idempotent if a² = a. Say R has characteristic 2 if a + a = 0 for all a € R. Prove that if R is a commutative ring with characteristic 2, then the set of all idempotent elements forms a subring.
Let R be a ring. Call an element a = R idempotent if a² = a. Say R has characteristic 2 if a + a = 0 for all a € R. Prove that if R is a commutative ring with characteristic 2, then the set of all idempotent elements forms a subring.
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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