Exam2Review - Math 302 Modern Algebra Spring 2009 Exam 2...

Info iconThis preview shows page 1. Sign up to view the full content.

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

Unformatted text preview: Math 302 Modern Algebra Spring 2009 Exam 2 Information Date: Friday, April 10 Covering: Chapter 3, Sections 1, 2, 3, 4 Chapter 4, Sections 1, 2, 3, 4, 5 Exam 2 Review Problems 1. Let R = { , a, b, c } with addition and multiplication defined by the following tables. It can be shown that R is a commutative ring. + a b c a b c a a c b b b c a c c b a a b c a a a b b b c a b c (a) Verify property R5 Existence of Additive Inverses. (b) Show that R satisfies R10 Existence of a Multiplicative Identity. (c) Is R a field? Justify your conclusion. 2. Let S be the set of integers with an addition and multiplication defined for all a, b S by a b = a + b 1 and a b = a b a b + 2 . (The +, , and symbols denote ordinary integer addition, subtraction, and multiplication, re- spectively.) (a) Show that S is a commutative ring. (b) Verify ring axioms R10 and R11 for S ....
View Full Document

Ask a homework question - tutors are online