Answered: Suppose that theta: R --> S is a ring…

Suppose that theta: R --> S is a ring homomorphism and that the image of theta is not {0}. If R has a unity and S is an integral domain, show that theta carries the unity of R to the unity of S.

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 32E: 32. Consider the set . a. Construct addition and multiplication tables for, using the...

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Question

Suppose that theta: R --> S is a ring homomorphism and that the image

of theta is not {0}. If R has a unity and S is an integral domain, show

that theta carries the unity of R to the unity of S.

Please be clear, detailed. Give math rules, theorems. Be legible.

Thank you.

With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.

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