1. Define a ring R to be the integers with the operationsab:= a + b 1ab:= a + b - ab,where the operations on the right are the usual operations on Z. Provethat R is a ring.

The given operations,The given set is the set of all integers.The aim is to prove that the set of…

Answered: Define a ring R to be the integers with…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.2: Ring Homomorphisms

Problem 19E

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Define a ring R to be the integers with the operations ab=a+b-1 ab:= a + b - ab, where the operations on the right are the usual operations on Z. Prove that Ris a ring.