Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $\Sigma$-semicommutative rings and their skew PBW extensions   In this paper, we introduce the concept of $\Sigma$-semicommutative ring, for
$\Sigma$ a finite family of endomorphisms of a ring $R$. We relate this class
of rings with other classes of rings such that Abelian, reduced,
$\Sigma$-rigid, nil-reversible and rings satisfying the $\Sigma$-skew reflexive
nilpotent property. Also, we study some ring-theoretical properties of skew PBW
extensions over $\Sigma$-semicommutative rings. We prove that if a ring $R$ is
$\Sigma$-semicommutative with certain conditions of compatibility on
derivations, then for every skew PBW extension $A$ over $R$, $R$ is Baer if and
only if $R$ is quasi-Baer, and equivalently, $A$ is quasi-Baer if and only if
$A$ is Baer. Finally, we consider some topological conditions for skew PBW
extensions over $\Sigma$-semicommutative rings.

18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
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The categories of this paper are: patt-sol
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The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
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The categories of this paper are: supr-con
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The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: bayes-an