Question 1. Let G = Q be the set of all rational numbers, and * = + be the usual addition operation on Q. Show that (Q, +) is a group. You need to show the following: 1. Closure: Q is closed under addition 2. Associativity: The addition operation is associative on Q 3. Identity: What is the identity element in (Q,+)? 4. Inverses: What is the additive inverse of each element in Q?

Question 1. Let G = Q be the set of all rational numbers, and * = + be the usual addition operation on Q. Show that (Q, +) is a group. You need to show the following: 1. Closure: Q is closed under addition 2. Associativity: The addition operation is associative on Q 3. Identity: What is the identity element in (Q,+)? 4. Inverses: What is the additive inverse of each element in Q?

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.7: Direct Sums (optional)

Problem 19E: 19. a. Show that is isomorphic to , where the group operation in each of , and is addition. ...

See similar textbooks