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Vietnam Journal of Mathematics 36:2(2008) 183-190 Primary Decomposition for Noncommutative Rings Hossain Khabazian Abstract.  A necessary condition for the existence of primary decomposition in noncommutative rings is investigated and its role is explored. Furthermore, the associated prime ideals are determined.   2000 Mathematics Subject Classification: 16D70, 16D25. Keywords: Prime ideal, primary ideal, primary decomposition, prime right annihilator, annihilator ideal.

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