Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Generalization Of Regular And Strongly $\Pi$-regular Rings   We introduce and investigate the so-called D-regularly nil clean rings by
showing that these rings are, in fact, a non-trivial generalization of the
classical von Neumann regular rings and of the strongly $\pi$-regular rings.
Some other close relationships with certain well-known classes of rings such as
$\pi$-regular rings, exchange rings, clean rings, nil-clean rings, etc., are
also demonstrated. These results somewhat supply a recent publication of the
author in Turk. J. Math. (2019) as well as they somewhat expand the important
role of the two examples of nil-clean rings obtained by Ster in Lin. Algebra \&
Appl. (2018). Likewise, the obtained symmetrization supports that for exchange
rings established by Khurana et al. in Algebras \& Represent. Theory (2015).

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The categories of this paper are: mtrl-th
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The categories of this paper are: math-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-th
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The categories of this paper are: patt-sol
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The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
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The categories of this paper are: q-alg
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ph
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The categories of this paper are: q-fin
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The categories of this paper are: comp-gas
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The categories of this paper are: cond-mat
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The categories of this paper are: gr-qc