Rings in which idempotents generate maximal or minimal ideals

被引：0
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作者：
Themba Dube
Mojtaba Ghirati
Sajad Nazari
Ali Taherifar
机构：
[1] University of South Africa,Department of Mathematical Sciences
[2] Yasouj University,Department of Mathematics
[3] University of Orléans,Insa Centre Val de Loire
来源：
Algebra universalis | 2020年 / 81卷
关键词：
Ring; Commutative ring; Maximal ideal; Maximal spectrum; Zariski topology; Minimal ideal; Idempotent; Boolean algebra; 03G05; 12E15; 13A15; 16B99; 54C40;
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摘要：
We characterize rings in which every left ideal generated by an idempotent different from 0 and 1 is either a maximal left ideal or a minimal left ideal. In the commutative case, we give a characterization in terms of topological properties of the maximal spectrum with the Zariski topology. We also consider a strictly weaker variant of this property, defined almost similarly, and characterize those rings that have the property in question.
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