Homogeneous nilradicals over semigroup graded rings |
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| Authors: | Chan Yong Hong Nam Kyun Kim Blake W Madill Pace P Nielsen Micha? Ziembowski |
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| Institution: | 1. Department of Mathematics and Research Institute for Basic Sciences, Kyung Hee University, Seoul 131-701, Republic of Korea;2. School of Basic Sciences, Hanbat National University, Daejeon 34158, Republic of Korea;3. Department of Pure Mathematics, University of Waterloo, Ontario, N2L 3G1 Canada;4. Department of Mathematics, Brigham Young University, Provo, UT 84602, USA;5. Faculty of Mathematics and Information Science, Warsaw University of Technology, 00-662 Warsaw, Poland |
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| Abstract: | In this paper we study the homogeneity of radicals defined by nilpotence or primality conditions, in rings graded by a semigroup S. When S is a unique product semigroup, we show that the right (and left) strongly prime and uniformly strongly prime radicals are homogeneous, and an even stronger result holds for the generalized nilradical. We further prove that rings graded by torsion-free, nilpotent groups have homogeneous upper nilradical. We conclude by showing that non-semiprime rings graded by a large class of semigroups must always contain nonzero homogeneous nilpotent ideals. |
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| Keywords: | Primary 16N40 16W50 secondary 16N20 16N60 16N80 20M10 06F05 |
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