9. Consider the set R = {[0], [2], [4], [6], [8]} C Z10. %3D a. Construct addition and multiplication tables for R, using the operations for Z10. (a] +[b] = [a + b] [a] • [b] = [ab] %3D b. Observe that R is a commutative ring with unity [6], and compare this unity with the unity in Z10. c. Is Ra subring of Z10? If not, give a reason.

9. Consider the set R = {[0], [2], [4], [6], [8]} C Z10. %3D a. Construct addition and multiplication tables for R, using the operations for Z10. (a] +[b] = [a + b] [a] • [b] = [ab] %3D b. Observe that R is a commutative ring with unity [6], and compare this unity with the unity in Z10. c. Is Ra subring of Z10? If not, give a reason.

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 32E: 32. Consider the set . a. Construct addition and multiplication tables for, using the...

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32. Consider the set . a. Construct addition and multiplication tables for, using the operations as defined in . b. Observe that is a commutative ring with unity, and compare this unity with the unity in . c. Is a subring of ? If not, give a reason. d. Does have zero divisors? e. Which elements of have multiplicative inverses?
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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