An element in a ring R with identity is said to be strongly nil clean if it is the sum of an idempotent and a nilpotent that commute, R is said to be strongly nil clean if every element of R is strongly nil clean. Let C(R) be the center of a ring R and g(x) be a fixed polynomial in C(R)[x]. Then R is said to be strongly g(x)-nil clean if every element in R is a sum of a nilpotent and a root of g(x) that commute. In this paper, we give some relations between strongly nil clean rings and strongly g(x)-nil clean rings. Various basic properties of strongly g(x) -nil cleans are proved and many examples are given.
@article{bwmeta1.element.doi-10_1515_math-2017-0031,
author = {Ali H. Handam and Hani A. Khashan},
title = {Rings in which elements are the sum of a nilpotent and a root of a fixed polynomial that commute},
journal = {Open Mathematics},
volume = {15},
year = {2017},
pages = {420-426},
zbl = {06715915},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_math-2017-0031}
}
Ali H. Handam; Hani A. Khashan. Rings in which elements are the sum of a nilpotent and a root of a fixed polynomial that commute. Open Mathematics, Tome 15 (2017) pp. 420-426. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_math-2017-0031/