nov15 - Math 3124 Tuesday, November 15 November 15,...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Math 3124 Tuesday, November 15 November 15, Ungraded Homework Problem 27.14 on page 135. What can be said about the characteristic of a ring R in which x =- x for each x R ? Since x =- x for all x R , by adding x to both sides we see that 2 x = 0 for all x R . Therefore the characteristic of R is at most 2; in other words it is 1 or 2. The characteristic being 1 means that R = { } . We conclude that either the characteristic of R is 2 or R is the zero ring. Section 38 on page 180. Which of the mappings in the following problems are ring homo- morphisms? Determine the kernel of each mapping that is a homomorphism. 1. : Z Z by ( a ) = 3 a This is not a homomorphism because does not respect multiplication. For example ( 1 * 1 ) = ( 1 ) = 3, yet ( 1 ) * ( 1 ) = 3 * 3 = 9. 2. : Z Z by ( a ) = a 2 This is not a homomorphism because does not respect addition. For example we have ( 1 + 1 ) = ( 1 + 1 ) 2 = 4, yet ( 1 )+ ( 1 ) = 1 + 1 = 2.2....
View Full Document

Page1 / 2

nov15 - Math 3124 Tuesday, November 15 November 15,...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online