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

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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 ....
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This note was uploaded on 10/20/2009 for the course MATH 302 taught by Professor Edwards during the Spring '03 term at CSU Fullerton.

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