Let R = {2n: n E Z} and define addition and multiplication O in R by a b = a + b and aOb = for all a,b e R. Under these operations, R is a ring. Show that this ring and the ring of integers are isomorphic.
Let R = {2n: n E Z} and define addition and multiplication O in R by a b = a + b and aOb = for all a,b e R. Under these operations, R is a ring. Show that this ring and the ring of integers are isomorphic.
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 21E: 21. Define a new operation of addition in by with a new multiplication in by.
a. Verify that...
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