Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 51, No. 1, pp. 57-61 (2010)

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Some small-centralizer properties for rings

Howard E. Bell and Abraham A. Klein

Department of Mathematics, Brock University, St. Catharines, Ontario, Canada L2S 3A1, e-mail:; School of Mathematical Sciences, Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel, e-mail:

Abstract: We characterize rings $R$ in which certain elements $x$ have the property that $C_{R}(x)$ (resp. the set of zero divisors in $C_{R}(x)$) is finite. We also explore the consequences of an assumption that certain $x$ satisfy $C_{R}(x) = \langle x \rangle$.

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Electronic version published on: 27 Jan 2010. This page was last modified: 28 Jan 2013.

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