Rings consisting entirely of certain elements |
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| Authors: | Huanyin Chen Marjan Sheibani Nahid Ashrafi |
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| Institution: | 1.Department of Mathematics,Hangzhou Normal University,Hangzhou,China;2.Women’s University of Semnan (Farzanegan),Semnan,Iran;3.Faculty of Mathematics, Statistics and Computer Science,Semnan University,Semnan,Iran |
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| 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; Z3 ⊕ Z3; Z3 ⊕ B where B is a Boolean ring; local ring with nil Jacobson radical; M2(Z2) or M2(Z3); or the ring of a Morita context with zero pairings where the underlying rings are Z2 or Z3. |
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