Don't copy For any element a in a ring R, define (a) to be the smallest ideal ofR that contains a. If R is a commutative ring with unity, show that(a) = aR = {ar |rER}. Show, by example, that if R is commuta-tive but does not have a unity, then (a) and aR may be different.

Name: Don't copy For any element a in a ring R, define (a) to be the smalles
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Description: Don't copy For any element a in a ring R, define (a) to be the smallest ideal ofR that contains a. If R is a commutative ring with unity, show that(a) = aR = {ar |rER}. Show, by example, that if R is commuta-tive but does not have a unity, then (a) a

An ideal is a non-empty sub set I of a ring R, such that

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For any element a in a ring R, define (a) to be the smallest ideal of R that contains a. If R is a commutative ring with unity, show that (a) = aR = {ar TrER}. Show, by example, that if R is commuta- tive but does not have a unity, then (a) and aR may be different.

For any element a in a ring R, define (a) to be the smallest ideal of R that contains a. If R is a commutative ring with unity, show that (a) = aR = {ar TrER}. Show, by example, that if R is commuta- tive but does not have a unity, then (a) and aR may be different.

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 49E: An element a of a ring R is called nilpotent if an=0 for some positive integer n. Prove that the set...

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