3.Let R be a ring. Suppose a subset S of R is a ring under the induced ring operationsof R.(a) If both are unitary rings, does it follow that 1r = 1s? Justify your claim.(b) If both are integral domains, does it follow that 1R = 15? Justify your claim.

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Answered: 3. Let R be a ring. Suppose a subset S…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.2: Integral Domains And Fields

Problem 15E: [Type here] 15. Give an example of an infinite commutative ring with no zero divisors that is not an...

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3. Let R be a ring. Suppose a subset S of R is a ring under the induced ring operations of R. (a) If both are unitary rings, does it follow that 1R = 1s? Justify your claim. (b) If both are integral domains, does it follow that 1R = 1g? Justify your claim.