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Serial Rings with T-Nilpotent Prime Radical

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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.

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Authors and Affiliations

  1. Institute of Econometrics and Computer Science, Technical University of Częstochowa, Armii Krajowej 19b, 42-200, Częstochowa, Poland

    N. M. Gubareni

  2. Department of Mechanics and Mathematics, Kyiv Taras Shevchenko University, Volodymyrs'ka 64, 01033, Kyiv, Ukraine

    V. V. Kirichenko

Authors
  1. N. M. Gubareni
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  2. V. V. Kirichenko
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Correspondence to N. M. Gubareni.

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Mathematics Subject Classifications (2000)

16P40, 16G10.

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Gubareni, N.M., Kirichenko, V.V. Serial Rings with T-Nilpotent Prime Radical. Algebr Represent Theor 9, 147–160 (2006). https://doi.org/10.1007/s10468-005-8759-6

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  • DOI: https://doi.org/10.1007/s10468-005-8759-6

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