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On Andrunakievich’s chain and Koethe’s problem

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Abstract

In 1969 Andrunakievich asked whether one gets a ring without nonzero nil left ideals from an arbitrary ring R by factoring out the ideal A(R) which is the sum of all nil left ideals of R. Recently, it was shown that this problem is equivalent to Koethe’s problem. In this context one may consider the chain of ideals, which starts with A 1(R) = A(R) ⊆ A 2(R), where A 2(R)/A 1(R) = A(R/A 1(R)), and extends by repeating this process. We study the properties of this chain and show that, assuming a negative solution of Koethe’s problem, this chain can terminate at any given ordinal number.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Kent State University Summit Street, Kent, Ohio, 44242, USA

    M. A. Chebotar

  2. Department of Mathematics, National Taiwan University, Taipei Office 1, Roosevelt Rd., Sec. 4, Taipei, 106, Taiwan

    P. -H. Lee

  3. National Center for Theoretical Sciences, Taipei Office 1, Roosevelt Rd., Sec. 4, Taipei, 106, Taiwan

    P. -H. Lee

  4. Institute of Mathematics, University of Warsaw, 02-097, Warsaw, Banacha 2, Poland

    E. R. Puczyłowski

Authors
  1. M. A. Chebotar
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  2. P. -H. Lee
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  3. E. R. Puczyłowski
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Corresponding author

Correspondence to M. A. Chebotar.

Additional information

Supported by MNiSW Grant No. N N201 268435 and National Center for Theoretical Sciences, Taipei Office, Taiwan.

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Chebotar, M.A., Lee, P.H. & Puczyłowski, E.R. On Andrunakievich’s chain and Koethe’s problem. Isr. J. Math. 180, 119–128 (2010). https://doi.org/10.1007/s11856-010-0096-8

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  • DOI: https://doi.org/10.1007/s11856-010-0096-8

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