Question 1. State whether True or False. Provide a reason in each case. (a) The pair (Z321.-) that consists of the set of congruence classes modulo 321 together with multiplication, has two zero divisors. (b) Every integral domain consists of an Abelian additive group, and a commutative unital ring which has a unity, but no zero divisors. (c) The set nZ for n € N, the set R\ Q. and the set C\R have no zero divisors.
Question 1. State whether True or False. Provide a reason in each case. (a) The pair (Z321.-) that consists of the set of congruence classes modulo 321 together with multiplication, has two zero divisors. (b) Every integral domain consists of an Abelian additive group, and a commutative unital ring which has a unity, but no zero divisors. (c) The set nZ for n € N, the set R\ Q. and the set C\R have no zero divisors.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter3: Groups
Section3.1: Definition Of A Group
Problem 51E: Prove that the Cartesian product 24 is an abelian group with respect to the binary operation of...
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