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ON *MP-CLEAN ELEMENT & MP-CLEAN RING*

Mohammed Dawood Salman Institute of Applied Arts, Middle Technical University, Baghdad, Iraq
Wissam Abbas Hussein General Directorate of Education of Salahuddin, Salahuddin, Iraq.
Ali Kadhim Yaqoob Department of Mathematics, College of Science, University of Anbar; Ramadi, Iraq.

Abstract

Impose that Ꞇ is unitary ring in this work paper we define another generalization of clean ring name mp-clean ring and show the connection between this concept and another clean rings (p-clean, m-clean, mj-clean). Where Ꞇ is mpclean ring if all elements in Ꞇ are mp-clean elements. some examples and properties of mp-clean ring gives, and we define another element say mp-clean element.

Keywords

Ring, Mp-Clean, M-Clean, Mj-Clean, Amalgamated, P-Clean.,