Let Z∗ be the set of integers together with ⊕ and ⊗ defined by a ⊕ b = a + b − 1 a ⊗ b = ab − a − b + 2. Show that Z∗ is a ring by finding an isomorphism from Z to Z∗. (Hint: What is the multiplicative identity in Z∗?)

Let Z∗ be the set of integers together with ⊕ and ⊗ defined by a ⊕ b = a + b − 1 a ⊗ b = ab − a − b + 2. Show that Z∗ is a ring by finding an isomorphism from Z to Z∗. (Hint: What is the multiplicative identity in Z∗?)

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

Let Z∗ be the set of integers together with ⊕ and ⊗ defined by
a ⊕ b = a + b − 1
a ⊗ b = ab − a − b + 2.
Show that Z∗ is a ring by finding an isomorphism from Z to Z∗. (Hint: What is the multiplicative
identity in Z∗?)

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