Czechoslovak Mathematical Journal

Czechoslovak Mathematical Journal, Vol. 68, No. 2, pp. 553-558, 2018

Rings consisting entirely of certain elements

Huanyin Chen, Marjan Sheibani, Nahid Ashrafi

Received October 20, 2016. First published March 22, 2018.

Abstract: We completely determine when a ring consists entirely of weak idempotents, units and nilpotents. We prove that such ring is exactly isomorphic to one of the following: a Boolean ring; $\Bbb Z_3\oplus{\Bbb Z}_3$; $\Bbb Z_3\oplus B$ where $B$ is a Boolean ring; local ring with nil Jacobson radical; $M_2(\Bbb Z_2)$ or $M_2(\Bbb Z_3)$; or the ring of a Morita context with zero pairings where the underlying rings are $\Bbb Z_2$ or $\Bbb Z_3$.

Keywords: idempotent; nilpotent; Boolean ring; local ring; Morita context

Classification MSC: 16U10, 16E50, 16S34

DOI: 10.21136/CMJ.2018.0554-16

PDF available at: Springer Institute of Mathematics CAS Digital Mathematics Library

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Affiliations: Huanyin Chen, Department of Mathematics, Hangzhou Normal University, Hangzhou, China, e-mail: huanyinchen@aliyun.com; Marjan Sheibani (corresponding author), Women's University of Semnan (Farzanegan), Semnan, Iran, e-mail: sheibani@fgusem.ac.ir; Nahid Ashrafi, Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran, e-mail: nashrafi@semnan.ac.ir

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