Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter5: Rings, Integral Domains, And Fields
Section5.1: Definition Of A Ring
Problem 15E: 15. Let and be elements of a ring. Prove that the equation has a unique solution.
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![Let R and S be rings, and let r ER and s E S. Prove that (r, s) is a unit in R × S if and only if r is a unit
in R and s is a unit in S.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faf4d5614-e5fa-4399-aabc-c345eeef0588%2F4ea8f806-2253-4433-b85c-58cb93ec7c24%2Ffuyl99_processed.png&w=3840&q=75)
Transcribed Image Text:Let R and S be rings, and let r ER and s E S. Prove that (r, s) is a unit in R × S if and only if r is a unit
in R and s is a unit in S.
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