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535 544 Bell, H. E. and Klein, A. A. , Noncommutativity and noncentral zero divisors, Internat. J. Math. & Math. Sci. 22 (1999), 67–74. MR 2000b

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References [1] Anderson , D. F. Livingston , P. S. 1999 The zero-divisor graph of commutative ring J

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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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] Huckaba , J. A. , Commutative rings with zero divisors , Marcel Dekker Inc. , New York , 1988 . [14] Hwang , S

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. , Commutative Rings with Zero-Divisors , Marcel Dekker , New York , 1988 . [11] Huckaba , J. A. and Keller , J. M. , Annihilation of ideals in Commutative rings , Pacific J

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A recently published paper [6] considered the total graph of commutative ring R. In this paper, we compute Wiener, hyper-Wiener, reverse Wiener, Randić, Zagreb, ABC and GA indices of zero-divisor graph.

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Acta Mathematica Hungarica
Authors: Afshin Amini, Babak Amini, Ehsan Momtahan, and Mohammad Hassan Shirdareh Haghighi

References [1] Akbari , S. Maimani , H. R. Yassemi , S. 2003 When a zero-divisor graph is planar or

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Abstract  

Connections between radicals of alternative and right alternative rings are investigated, with emphasis on those which are nondegenerate in the sense that semi-simple rings have no absolute zero-divisors. In particular it is shown that nondegenerate radicals of right alternative rings have the Anderson-Divinsky-Sulinski property.

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] Anderson , D. F. Livingston , P. S. 1999 The zero-divisor graph of a commutative ring J. Algebra 217 434 – 447 10.1006/jabr.1998

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