Abstract
In this paper, we introduce the notions of m-clean and strongly m-clean ring as generalizations of clean ring and strongly clean ring respectively. We prove that if a ring R is m-clean then the matrix ring is also m-clean. We provide a characterization of strongly m-clean ring in terms of quotient ring by its ideal which is contained in its Jacobson radical. In particular, we prove that a ring is strongly m-clean if and only if its quotient ring by a nil ideal is strongly m-clean under certain conditions. We also introduce the notion of m-local ring as a subclass of local ring. We establish that a ring is m-local if and only if it is m-clean and it has no non-trivial m-potent element.
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