Let Z* be the set of non-zero integers. In this problem you look at questions about division on the set Z". (a) Is divis

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Let Z Be The Set Of Non Zero Integers In This Problem You Look At Questions About Division On The Set Z A Is Divis 1 (52.57 KiB) Viewed 72 times

Let Z* be the set of non-zero integers. In this problem you look at questions about division on the set Z". (a) Is division closed on Z*? Explain your answer. (b) Is division associative on Z*? Explain your answer. (c) Is division commutative on Z*? Explain your answer. (d) Show that 1 is a right identity element for division on Z*. (e) Does division on Z* have a left identity element? In other words, can you find a (fixed) non-zero integer z such that 2 : a = a for all a € Z"? (f) Which elements of Z* have a right inverse under division? In other words, which values of n have a solution to the equation n : ___ = 1 that lies in Z*? (g) Which elements of Z' have a left inverse under division? In other words, which values of n have a solution to the equation in=1 that lies in Z"? (h) Is (Z",) a group? Why or why not? (Use your answers to the previous questions to answer this question.)