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Miklós Schweitzer 1960- Problem 9

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November 21, 2015
college contests

Problem Statement

9. Let A1,…,AnA_1, \dots , A_n and BB be ideals of an assoticative ring RR such that BB is contained in the set-union of the ideals AiA_i(i=1,…,ni=1, \dots , n) but not contained in the union of any n−1n-1 of the ideals AiA_i. Show that, for some positive integer kk, BkB_k is contained in the intersection of the ideals AiA_i. (A. 19)
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