Question 5. Given the triple F = F(Q), +, > that consists of the set (Q) of all mappings a: QxQQ, together with the standard addition + and multiplication for such mappings. That is, (a+B)(x, y) = a(r,y)+(x, y), (a-B)(r,y)= a(r,y)B(r,y), Va, BEF(Q), Vr, ye Q. (a) Show that associativity holds under addition and multiplication of mappings. (b) Hence prove that the triple F=F(Q), +, constitutes a commutative ring. . (b) Let (Q) denote the set of all mappings a EF(Q) such that a(0, 0) = 0. Prove or disprove: The triple F=(Q), +, is a commutative ring.

Question 5. Given the triple F = F(Q), +, > that consists of the set (Q) of all mappings a: QxQQ, together with the standard addition + and multiplication for such mappings. That is, (a+B)(x, y) = a(r,y)+(x, y), (a-B)(r,y)= a(r,y)B(r,y), Va, BEF(Q), Vr, ye Q. (a) Show that associativity holds under addition and multiplication of mappings. (b) Hence prove that the triple F=F(Q), +, constitutes a commutative ring. . (b) Let (Q) denote the set of all mappings a EF(Q) such that a(0, 0) = 0. Prove or disprove: The triple F=(Q), +, is a commutative ring.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.2: Mappings

Problem 5E: 5. For each of the following mappings, determine whether the mapping is onto and whether it is...

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