Unformatted text preview: elements { a 1 , a 2 , . . . , a n } . If any element in this set is the identity, we are done. Otherwise, there are two elements in the set above, say a s and a t , that are the same. Then a ts is the identity element and is part of the set. Hence, we are done. (6) Problem 4 page 390. [graded] Solution: Let d be the order of a and let m be such that a m = 1. Say, m = dq + r , where 0 r &lt; d . Then, 1 = a m = a dq + r = ( a d ) q a r = a r , which implies that r = 0 since d was the smallest positive power of a that gives 1. Thus, d  m . 1...
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 Spring '08
 BILLERA
 Algebra, Ring, HW 12 Solutions

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