On strongly m-clean rings and m-semiperfect rings

Abstract

In this article, we continue the study of strongly m-clean ring which we introduced in the paper “On m-clean and strongly m-clean rings” (Purkait et al. 2020). Mainly, we characterize strongly m-clean ring in terms of m-semiperfect ring. For that, we introduce the notion of m-semiperfect ring and establish some results on this ring. We prove that under certain conditions a ring is m-semiperfect if and only if it is strongly m-clean and orthogonally m-finite.

Keywords:

• Clean ring
• m-clean ring
• m-semiperfect ring
• strongly clean ring
• strongly m-clean ring

AMS MATHEMATICS SUBJECT CLASSIFICATION (2010):

• 16U99
• 16Z05

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.

Acknowledgement

The research of the author is funded by UGC (DS Kothari PDF) (Award Letter No. F.4-2/2006 (BSR)/MA/15-16/0029), Govt. of India. The author is grateful to Prof. Tapan Kumar Dutta and Dr. Sukhendu Kar for their constant effort to enrich this article. The author is also thankful to the Department of Pure Mathematics, University of Calcutta, for providing necessary facilities for research.