Note on Strongly Nil Clean Elements in Rings
Abstract
Let R be an associative unital ring and let a R be a strongly nil clean element. We introduce a new idea for examining the properties of these elements. This approach allows us to generalize some results on nil clean and strongly nil clean rings. Also, using this technique many previous proofs can be significantly shortened. Some shorter proofs concerning nil clean elements in rings in general, and in matrix rings in particular, are presented, together with some generalizations of these results.
Keywords:
nilpotent element / nil clean elementSource:
Czechoslovak Mathematical Journal, 2019, 69, 1, 87-92Publisher:
- Springer New York LLC
Projects:
- Analysis and algebra with applications (RS-174032)
DOI: 10.21136/CMJ.2018.0167-17
ISSN: 0011-4642