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Commutativity results for periodic rings

Acta Mathematica Hungarica
Volume/Issue:
Volume 58: Issue 3-4
DOI:
https://doi.org/10.1007/bf01903957
Author: H. Abu-Khuzam
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Weakly periodic rings with conditions on commutators

Acta Mathematica Hungarica
Volume/Issue:
Volume 71: Issue 1-2
DOI:
https://doi.org/10.1007/bf00052203
Authors: H. Abu-Khuzam, M. Hasanali, and A. Yaqub
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Some commutativity results for periodic rings

Acta Mathematica Hungarica
Volume/Issue:
Volume 28: Issue 3-4
DOI:
https://doi.org/10.1007/bf01896791
Author: H. E. Bell
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On commutativity of periodic rings and near-rings

Acta Mathematica Hungarica
Volume/Issue:
Volume 36: Issue 3-4
DOI:
https://doi.org/10.1007/bf01898145
Author: H. E. Bell
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Almost-Commutativity in Rings

Acta Mathematica Hungarica
Volume/Issue:
Volume 96: Issue 1-2
DOI:
https://doi.org/10.1023/a:1015665612246
Authors: H. Bell and A. Klein

Abstract  

A subset X of the ring

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$R$$ \end{document}
is called almost commutative if
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$X\backslash C_R \left( a \right)$$ \end{document}
is finite for all
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$a \in X$$ \end{document}
. We study commutativity in rings in which certain infinite sets of zero divisors are almost commutative.

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Weakly periodic-like rings and commutativity

Studia Scientiarum Mathematicarum Hungarica
Volume/Issue:
Volume 43: Issue 3
DOI:
https://doi.org/10.1556/sscmath.43.2006.3.1
Author: Adil Yaqub

Bell, H. E., A commutativity study for periodic rings, Pacific J. Math. 70 (1977), no. 1, 29-36. MR 58 #793 A commutativity study for periodic rings Pacific J. Math

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A note on strongly π-regular rings

Acta Mathematica Hungarica
Volume/Issue:
Volume 102: Issue 4
DOI:
https://doi.org/10.1023/b:amhu.0000024683.13344.cf
Author: A. Chin

Abstract  

Let R be an associative ring with unit and let N(R) denote the set of nilpotent elements of R. R is said to be stronglyπ-regular if for each x∈R, there exist a positive integer n and an element y∈R such that x n=x n +1 y and xy=yx. R is said to be periodic if for each x∈R there are integers m,n≥ 1 such that m≠n and x m=x n. Assume that the idempotents in R are central. It is shown in this paper that R is a strongly π-regular ring if and only if N(R) coincides with the Jacobson radical of R and R/N(R) is regular. Some similar conditions for periodic rings are also obtained.

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