On prime ideals and radicals of polynomial rings and graded rings |
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Authors: | P-H Lee ER Puczy?owski |
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Institution: | 1. Department of Mathematics, National Taiwan University, Taipei 106, Taiwan;2. Institute of Mathematics, University of Warsaw, Warsaw, Poland |
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Abstract: | We extend some known results on radicals and prime ideals from polynomial rings and Laurent polynomial rings to Z-graded rings, i.e, rings graded by the additive group of integers. The main of them concerns the Brown–McCoy radical G and the radical S, which for a given ring A is defined as the intersection of prime ideals I of A such that A/I is a ring with a large center. The studies are related to some open problems on the radicals G and S of polynomial rings and situated in the context of Koethe’s problem. |
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Keywords: | 16W50 16N60 16N40 16D25 |
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