Feebly Baer Rings and Modules |
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| Authors: | M. Tamer Koşan Tsiu-Kwen Lee Yiqiang Zhou |
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| Affiliation: | 1. Department of Mathematics , Gebze Institute of Technology , Gebze/Kocaeli , Turkey mtkosan@gyte.edu.tr;3. Department of Mathematics , National Taiwan University , Taipei , Taiwan;4. Department of Mathematics and Statistics , Memorial University of Newfoundland , St. John's , Newfoundland , Canada |
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| Abstract: | A right module M over a ring R is called feebly Baer if, whenever xa = 0 with x ∈ M and a ∈ R, there exists e2 = e ∈ R such that xe = 0 and ea = a. The ring R is called feebly Baer if RR is a feebly Baer module. These notions are motivated by the commutative analog discussed in a recent paper by Knox, Levy, McGovern, and Shapiro [6 Knox , M. L. , Levy , R. , McGovern , W. Wm. , Shapiro , J. ( 2009 ) Generalizations of complemented rings with applications to rings of functions. . J. Alg. Appl. 8 ( 1 ): 17 – 40 .[Crossref] , [Google Scholar]]. Basic properties of feebly Baer rings and modules are proved, and their connections with von Neumann regular rings are addressed. |
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| Keywords: | Feebly Baer ring and module Von Neumann regular ring p.p. ring and module Triangular matrix ring polynomial modules |
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