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On the base radical class for associative rings

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Abstract

The base radical class L b(X), generated by a class X was introduced in [12]. It consists of those rings whose nonzero homomorphic images have nonzero accessible subrings in X. When X is homomorphically closed, L b(X) is the lower radical class defined by X, but otherwise X may not be contained in L b(X). We prove that for a hereditary radical class L with semisimple class S(R), L b(S(R)) is the class of strongly R-semisimple rings if and only if R is supernilpotent or subidempotent. A number of further examples of radical classes of the form L b(X) are discussed.

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Authors and Affiliations

  1. Discipline of Mathematics, University of Tasmania, GPO Box 252-37, Hobart, Tasmania, 001, Australia

    B. J. Gardner

  2. School of Mathematical and Decision Sciences, Central Queensland University, Rockhampton, Queensland, 4702, Australia

    R. G. McDougall

Authors
  1. B. J. Gardner
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  2. R. G. McDougall
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Gardner, B.J., McDougall, R.G. On the base radical class for associative rings. Acta Mathematica Hungarica 98, 263–272 (2003). https://doi.org/10.1023/A:1022882010815

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