Morphic rings and unit regular rings |
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Authors: | Tsiu-Kwen Lee Yiqiang Zhou |
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Institution: | a Department of Mathematics, National Taiwan University, Taipei 106, Taiwan b Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, Newfoundland A1C 5S7, Canada |
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Abstract: | A ring R is called left morphic if for every a∈R. A left and right morphic ring is called a morphic ring. If Mn(R) is morphic for all n≥1 then R is called a strongly morphic ring. A well-known result of Erlich says that a ring R is unit regular iff it is both (von Neumann) regular and left morphic. A new connection between morphic rings and unit regular rings is proved here: a ring R is unit regular iff Rx]/(xn) is strongly morphic for all n≥1 iff Rx]/(x2) is morphic. Various new families of left morphic or strongly morphic rings are constructed as extensions of unit regular rings and of principal ideal domains. This places some known examples in a broader context and answers some existing questions. |
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Keywords: | Primary 16E50 16U99 secondary 16S70 16S35 |
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