Geodesic
Rings consisting entirely of certain elements
Czechoslovak Mathematical Journal, Tome 68 (2018) no. 2, pp. 553-558
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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 $\Bbb Z_3$.
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 $\Bbb Z_3$.
DOI : 10.21136/CMJ.2018.0554-16
Classification : 16E50, 16S34, 16U10
Keywords: idempotent; nilpotent; Boolean ring; local ring; Morita context 
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Chen, Huanyin; Sheibani, Marjan; Ashrafi, Nahid. Rings consisting entirely of certain elements. Czechoslovak Mathematical Journal, Tome 68 (2018) no. 2, pp. 553-558. doi: 10.21136/CMJ.2018.0554-16

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