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 unitin R and s is a unit in S.

Answer Explanation:Step 1: Step 2: Step 3: Step 4:

Answered: Let R and S be rings, and let r ER and…

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.