The set of equivalence classes Zn = {[0], [1], - - · , [n – 1]} is an example of what is...called a finite ring (which simply means the elements can be added and multiplied in familiarways).(Def.) Two non-zero elements a and b in a ring are called zero divisors if a·b = 0. For example,in Z12 the elements [2] and [6] are zero divisors. Prove the following theorem.Theorem. If n is composite, then there exists at least one pair of zero divisors in Zn.

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Answered: The set of equivalence classes Zn =…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.1: Ideals And Quotient Rings

Problem 30E: a. For a fixed element a of a commutative ring R, prove that the set I={ar|rR} is an ideal of R....

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