Let R and S be commutative rings. Prove that (a, b) is a zero-divisorin R ⨁ S if and only if a or b is a zero-divisor or exactly one of a orb is 0.
Let R and S be commutative rings. Prove that (a, b) is a zero-divisorin R ⨁ S if and only if a or b is a zero-divisor or exactly one of a orb is 0.
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 10E: Let R be a commutative ring with characteristic 2. Show that each of the following is true for all...
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Let R and S be commutative rings. Prove that (a, b) is a zero-divisor
in R ⨁ S if and only if a or b is a zero-divisor or exactly one of a or
b is 0.
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