# Rings in which elements are the sum of a nilpotent and a root of a fixed polynomial that commute

Open Mathematics (2017)

• Volume: 15, Issue: 1, page 420-426
• ISSN: 2391-5455

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## Abstract

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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.

## How to cite

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Ali H. Handam, and Hani A. Khashan. "Rings in which elements are the sum of a nilpotent and a root of a fixed polynomial that commute." Open Mathematics 15.1 (2017): 420-426. <http://eudml.org/doc/288146>.

@article{AliH2017,
abstract = {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.},
author = {Ali H. Handam, Hani A. Khashan},
journal = {Open Mathematics},
keywords = {Nil clean ring; Strogly nil clean ring; g(x)-nil clean ring; Strongly g(x)-nil clean ring; nil clean ring; strogly nil clean ring; -nil clean ring; strongly $g(x)$-nil clean ring},
language = {eng},
number = {1},
pages = {420-426},
title = {Rings in which elements are the sum of a nilpotent and a root of a fixed polynomial that commute},
url = {http://eudml.org/doc/288146},
volume = {15},
year = {2017},
}

TY - JOUR
AU - Ali H. Handam
AU - Hani A. Khashan
TI - Rings in which elements are the sum of a nilpotent and a root of a fixed polynomial that commute
JO - Open Mathematics
PY - 2017
VL - 15
IS - 1
SP - 420
EP - 426
AB - 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.
LA - eng
KW - Nil clean ring; Strogly nil clean ring; g(x)-nil clean ring; Strongly g(x)-nil clean ring; nil clean ring; strogly nil clean ring; -nil clean ring; strongly $g(x)$-nil clean ring
UR - http://eudml.org/doc/288146
ER -

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