Let R be a commutative ring with identity. Using the homomorphism theorem (Theorem 16.45) and Proposition 16.32, show that an ideal M of R is maximal if and only if R/M is a field.
Let R be a commutative ring with identity. Using the homomorphism theorem (Theorem 16.45) and Proposition 16.32, show that an ideal M of R is maximal if and only if R/M 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 10E: Since this section presents a method for constructing a field of quotients for an arbitrary integral...
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Let R be a commutative ring with identity. Using the homomorphism theorem (Theorem 16.45) and Proposition 16.32, show that an ideal M of R is maximal if and only if R/M is a field.
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