ISSN 1997-7670 (Print)
ISSN 2541-8785 (Online)

List of issues > Series «Mathematics». 2019. Vol. 27

Left-Right Cleanness and Nil Cleanness in Unital Rings

P. V. Danchev

We introduce the notions of left and right cleanness and nil cleanness in rings showing their close relationships with the classical concepts of cleanness and nil cleanness. Specifically, it is proved that strongly clean rings are both L-clean and R-clean as well as strongly nil clean rings are both L-nil clean and R-nil clean. These two assertions somewhat strengthen well-known results due to Nicholson (Comm. Algebra, 1999) and Diesl (J. Algebra, 2013). Moreover, it is shown that L-nil cleanness (respectively, R-nil cleanness) is preserved modulo nil Jacobson radical as well as that this is still true for L-cleanness (respectively, R-cleanness), provided the Jacobson radical is nil.

About the Authors

Peter Vassilev Danchev, Ph.D. (Math.), Prof., Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev st., bl. 8, Sofia, 1113, Bulgaria, e-mail: danchev@math.bas.bg; pvdanchev@yahoo.com

For citation

Danchev P.V. Left-Right Cleanness and Nil Cleanness in Unital Rings. The Bulletin of Irkutsk State University. Series Mathematics, 2019, vol. 27, pp. 28-35. https://doi.org/10.26516/1997-7670.2019.27.28

clean rings, nil clean rings, L-clean rings, R-clean rings, L-nil clean rings, R-nil clean rings.
16U99; 16E50; 13B99
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