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Properties of Generalized Nilpotent Elements of Pseudo-Normed Commutative Rings

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Abstract

The set I of all generalized nilpotent elements of a pseudo-normed commutative ring (R, ξ) is a closed ideal, and the factor ring (R, ξ)/I does not contain nonzero generalized nilpotent elements.

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References

  1. S. A. Aleschenko and V. I. Arnautov, “Quotient rings of pseudo-normed rings,” Bull. Acad. Sci. Rep. Moldova. Math., 44, No. 1, 3–16 (2006).

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  2. M. M. Gelfand, D. A. Raikov, and G. E. Shilov, Commutative Normed Rings [in Russian], Fizmatgiz, Moscow (1960).

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Authors and Affiliations

  1. Taras Shevchenko Transnistria State University, Tiraspol, Transnistria, Moldova

    S. A. Aleschenko

  2. Institute of Mathematics and Computer Science, Academy of Sciences of Moldova, Chisinau, Moldova

    V. I. Arnautov

  3. Moscow Lomonosov State University, Moscow, Russia

    S. T. Glavatsky

Authors
  1. S. A. Aleschenko
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  2. V. I. Arnautov
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  3. S. T. Glavatsky
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Corresponding author

Correspondence to S. A. Aleschenko.

Additional information

Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 23, No. 3, pp. 3–11, 2020.

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Aleschenko, S.A., Arnautov, V.I. & Glavatsky, S.T. Properties of Generalized Nilpotent Elements of Pseudo-Normed Commutative Rings. J Math Sci 269, 269–275 (2023). https://doi.org/10.1007/s10958-023-06276-6

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  • DOI: https://doi.org/10.1007/s10958-023-06276-6

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