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Let n > 1 be an integer. We say that [x] E Z/n is a zero divisor if there ex- ists [y] E Z /n – {[0]} such that [x][y] = [0]. We say that [æ] is a unit if there exists [y] E Z /n such that [x][y] = [1]. 7a) What are all the units in Z/12? What are all the zero divisors? b) What are all the units in Z/14? What are all the zero divisors? c) What are all the units in Z/13? What are all the zero divisors? (You do not need to prove your answers to this question, but you should show your work.)

Let n > 1 be an integer. We say that [x] E Z/n is a zero divisor if there ex- ists [y] E Z /n – {[0]} such that [x][y] = [0]. We say that [æ] is a unit if there exists [y] E Z /n such that [x][y] = [1]. 7a) What are all the units in Z/12? What are all the zero divisors? b) What are all the units in Z/14? What are all the zero divisors? c) What are all the units in Z/13? What are all the zero divisors? (You do not need to prove your answers to this question, but you should show your work.)

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter6: More On Rings
Section6.3: The Characteristic Of A Ring
Problem 9E: Let D be an integral domain with four elements, D=0,e,a,b, where e is the unity. a. Prove that D has...
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Let n > 1 be an integer. We say that [x] E Z/n is a zero divisor if there ex- ists [y] e Z/n – {[0]} such that ["]Y) exists [y] E Z /n such that [x][y] = [1]. [0]. We say that [x] is a unit if there 7a) What are all the units in Z/12? What are all the zero divisors? b) What are all the units in Z/14? What are all the zero divisors? c) What are all the units in Z/13? What are all the zero divisors? (You do not need to prove your answers to this question, but you should show your work.)
Transcribed Image Text:Let n > 1 be an integer. We say that [x] E Z/n is a zero divisor if there ex- ists [y] e Z/n – {[0]} such that ["]Y) exists [y] E Z /n such that [x][y] = [1]. [0]. We say that [x] is a unit if there 7a) What are all the units in Z/12? What are all the zero divisors? b) What are all the units in Z/14? What are all the zero divisors? c) What are all the units in Z/13? What are all the zero divisors? (You do not need to prove your answers to this question, but you should show your work.)
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