| On m-clean rings and M-clean graphs |
| Paper ID : 1042-ISCH |
| Authors |
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Aya Gamal Ali *1, Susan F. El-Deken2, Harlad Fripertinger3 1Mathematical department, faculty of science, Helwan university,Giza,Egypt 2Department of Mathematics, Faculty of science, Helwan University 3NAWI-Graz Universit¨at Graz |
| Abstract |
| The aim of this paper is to introduce and study some of the basic properties of the notion of M-clean graph which is a generalization of clean graph. We also provide a characterization of M-clean graphs. Also, studying some of its subgraphs MCl1(R) and MCl2(R). An M-clean graph of R is a graph whose vertices are related to m-clean elements of R.The set M be the set of all m-potent elements of R (i.e. r ∈ M if and only if r^m = r). basic of definition: An element x ∈ R is said to be m-clean if x can be written as x = r + u; where u ∈ U (R) and r ∈ M. M-clean graph of R is a graph whose vertices are related to m-clean elements of R. Note that a m-clean element of R may have two presentation in the form x = r + u = s + v. |
| Keywords |
| clean ring m-clean ring Clean graph M-Clean graph |
| Status: Abstract Accepted (Oral Presentation) |