(2) For each of the following sets, which of the axioms of a field, listed in Theorem 1.1. of our text (page 5), do not hold if one replaces Q with the indicated set? Explain. (a) The set of non-negative integers {0,1,2,3, ...}. (b) The set of non-negative rational numbers {q E Q | q > 0}. (c) The set of all integers Z = {.…..,-2, –1,0, 1, 2, ...}.

(2) For each of the following sets, which of the axioms of a field, listed in Theorem 1.1. of our text (page 5), do not hold if one replaces Q with the indicated set? Explain. (a) The set of non-negative integers {0,1,2,3, ...}. (b) The set of non-negative rational numbers {q E Q | q > 0}. (c) The set of all integers Z = {.…..,-2, –1,0, 1, 2, ...}.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter8: Polynomials

Section8.2: Divisibility And Greatest Common Divisor

Problem 35E

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