On graded nil clean rings

ABSTRACT

In this paper we introduce and study the notion of a graded (strongly) nil clean ring which is group graded. We also deal with extensions of graded (strongly) nil clean rings to graded matrix rings and to graded group rings. The question of when nil cleanness of the component, which corresponds to the neutral element of a group, implies graded nil cleanness of the whole graded ring is examined. Similar question is discussed in the case of groupoid graded rings as well.

KEYWORDS:

• Graded rings and modules
• group rings
• matrix rings
• nil clean rings

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 16W50
• 16U99
• 16S34
• 16S50

Acknowledgments

The authors would like to express their sincere gratitude to Professor Ivan Shestakov and to the referee for handling this manuscript.