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

• Autorzy: Ali H. Handam , Hani A. Khashan
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Nil clean ring; Strogly nil clean ring; g(x)-nil clean ring; Strongly g(x)-nil clean ring

Kategorie tematyczne

• 16U99: None of the above, but in this section
• 16N40: Nil and nilpotent radicals, sets, ideals, rings

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2017
• Tom: 15
• Numer: 1
• Strony: 420-426

Daty

wydano

2017-01-01

otrzymano

2016-01-12

zaakceptowano

2017-02-02

online

2017-04-17

Twórcy

autor

Ali H. Handam

• Department of Mathematics, Al al-Bayt University, P.O.Box: 130095, Al Mafraq,

autor

Hani A. Khashan

• Department of Mathematics, Al al-Bayt University, P.O.Box: 130095, Al Mafraq,

Identyfikatory

DOI

10.1515/math-2017-0031