Let T = { | EQ, a and b are relatively prime and 5 does not divide b}. Show that T is a ring under the usual addition and multiplication. Also, prove that I {ET | 5 divides a} is an ideal of T and the quotient ring T/I is a field. -

Let T = { | EQ, a and b are relatively prime and 5 does not divide b}. Show that T is a ring under the usual addition and multiplication. Also, prove that I {ET | 5 divides a} is an ideal of T and the quotient ring T/I is a field. -

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.3: The Field Of Quotients Of An Integral Domain

Problem 16E: Prove that any field that contains an intergral domain D must contain a subfield isomorphic to the...

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Question

Let T = {| EQ, a and b are relatively prime and 5 does not divide b}.
Show that T is a ring under the usual addition and multiplication. Also,
prove that I = {ET | 5 divides a} is an ideal of T and the quotient
ring T/I is a field.

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