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

Ali H. Handam; Hani A. Khashan

Open Mathematics (2017)

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

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topAli 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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