Rings in which elements are the sum of a nilpotent and a root of a fixed polynomial that commute
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 i...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2017-04-01
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| Series: | Open Mathematics |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/math-2017-0031 |
| _version_ | 1818689916031205376 |
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| author | Handam Ali H. Khashan Hani A. |
| author_facet | Handam Ali H. Khashan Hani A. |
| author_sort | Handam Ali H. |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-17T12:17:42Z |
| format | Article |
| id | doaj.art-3dc0cf4d82324e2cae047b436c22b419 |
| institution | Directory Open Access Journal |
| issn | 2391-5455 |
| language | English |
| last_indexed | 2024-12-17T12:17:42Z |
| publishDate | 2017-04-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj.art-3dc0cf4d82324e2cae047b436c22b4192022-12-21T21:49:06ZengDe GruyterOpen Mathematics2391-54552017-04-0115142042610.1515/math-2017-0031math-2017-0031Rings in which elements are the sum of a nilpotent and a root of a fixed polynomial that commuteHandam Ali H.0Khashan Hani A.1Department of Mathematics, Al al-Bayt University, P.O.Box: 130095, Al Mafraq, JordanDepartment of Mathematics, Al al-Bayt University, P.O.Box: 130095, Al Mafraq, JordanAn 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.https://doi.org/10.1515/math-2017-0031nil clean ringstrogly nil clean ringg(x)-nil clean ringstrongly g(x)-nil clean ring16n4016u99 |
| spellingShingle | Handam Ali H. Khashan Hani A. Rings in which elements are the sum of a nilpotent and a root of a fixed polynomial that commute Open Mathematics nil clean ring strogly nil clean ring g(x)-nil clean ring strongly g(x)-nil clean ring 16n40 16u99 |
| title | Rings in which elements are the sum of a nilpotent and a root of a fixed polynomial that commute |
| title_full | Rings in which elements are the sum of a nilpotent and a root of a fixed polynomial that commute |
| title_fullStr | Rings in which elements are the sum of a nilpotent and a root of a fixed polynomial that commute |
| title_full_unstemmed | Rings in which elements are the sum of a nilpotent and a root of a fixed polynomial that commute |
| title_short | Rings in which elements are the sum of a nilpotent and a root of a fixed polynomial that commute |
| title_sort | rings in which elements are the sum of a nilpotent and a root of a fixed polynomial that commute |
| topic | nil clean ring strogly nil clean ring g(x)-nil clean ring strongly g(x)-nil clean ring 16n40 16u99 |
| url | https://doi.org/10.1515/math-2017-0031 |
| work_keys_str_mv | AT handamalih ringsinwhichelementsarethesumofanilpotentandarootofafixedpolynomialthatcommute AT khashanhania ringsinwhichelementsarethesumofanilpotentandarootofafixedpolynomialthatcommute |