Can someone please help me understand the following problem. I need to know how to start the problem. i need to know the theorems ,identities, used please thank you. 6. Find an integer n that shows that the rings Z, need not have the fol-lowing properties that the ring of integers has.a. a? = a implies a = 0 or a = 1.b. ab = 0 implies a = 0 or b = 0.c. ab = ac and a + 0 imply b = c.Is the n you ound prime?

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Description: Can someone please help me understand the following problem. I need to know how to start the problem. i need to know the theorems ,identities, used please thank you. 6. Find an integer n that shows that the rings Z, need not have the fol-lowing prop

A ring is a set which satisfies properties like multiplicative identities and additive inverses.

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6. Find an integer n that shows that the rings Z, need not have the fol- lowing properties that the ring of integers has. a. a? = a implies a = 0 or a = 1. b. ab = 0 implies a = 0 or b = 0. c. ab = ac and a + 0 imply b = c. Is the n you ound prime?

6. Find an integer n that shows that the rings Z, need not have the fol- lowing properties that the ring of integers has. a. a? = a implies a = 0 or a = 1. b. ab = 0 implies a = 0 or b = 0. c. ab = ac and a + 0 imply b = c. Is the n you ound prime?

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 33E: Consider the set S={ [ 0 ],[ 2 ],[ 4 ],[ 6 ],[ 8 ],[ 10 ],[ 12 ],[ 14 ],[ 16 ] }18. Using addition...

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Consider the set S={ [ 0 ],[ 2 ],[ 4 ],[ 6 ],[ 8 ],[ 10 ],[ 12 ],[ 14 ],[ 16 ] }18. Using addition and multiplication as defined in 18, consider the following questions. Is S a ring? If not, give a reason. Is S a commutative ring with unity? If a unity exists, compare the unity in S with the unity in 18. Is S a subring of 18? If not, give a reason. Does S have zero divisors? Which elements of S have multiplicative inverses?
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