Serial Rings with T-Nilpotent Prime Radical |
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| Authors: | N. M. Gubareni V. V. Kirichenko |
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| Affiliation: | (1) Institute of Econometrics and Computer Science, Technical University of Częstochowa, Armii Krajowej 19b, 42-200 Częstochowa, Poland;(2) Department of Mechanics and Mathematics, Kyiv Taras Shevchenko University, Volodymyrs'ka 64, 01033 Kyiv, Ukraine |
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| Abstract: | In this paper we consider serial rings with T-nilpotent prime radical, factor-rings of which by the prime radical are right Noetherian rings. We prove that the prime quiver of such a ring is a disconnected union of cycles and chains. In the case when the prime quiver of such a serial ring is a chain the prime radical is nilpotent. For serial rings with nilpotent prime radical we introduce an analogue of Kupisch series. Presented by Yu. Drozd Mathematics Subject Classifications (2000) 16P40, 16G10. |
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| Keywords: | serial rings piecewise Noetherian ring prime radical quiver and prime quiver generalized Kupisch series |
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