Rings Whose Non-Invertible Elements Are Strongly Nil-Clean
We consider in-depth and characterize in certain aspects those rings whose non-units are strongly nil-clean in the sense that they are a sum of a commuting nilpotent and an idempotent. In addition, we examine those rings in which the non-units are uniquely nil-clean in the sense that they are a sum...
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| Published in | Lobachevskii journal of mathematics Vol. 45; no. 10; pp. 4980 - 5001 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
Moscow
Pleiades Publishing
01.10.2024
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1995-0802 1818-9962 |
| DOI | 10.1134/S1995080224602649 |
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| Abstract | We consider in-depth and characterize in certain aspects those rings whose non-units are strongly nil-clean in the sense that they are a sum of a commuting nilpotent and an idempotent. In addition, we examine those rings in which the non-units are uniquely nil-clean in the sense that they are a sum of a nilpotent and an unique idempotent. In fact, we succeeded to prove that these two classes of rings can completely be characterized in terms of already well-studied and fully described sorts of rings. |
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| AbstractList | We consider in-depth and characterize in certain aspects those rings whose non-units are strongly nil-clean in the sense that they are a sum of a commuting nilpotent and an idempotent. In addition, we examine those rings in which the non-units are uniquely nil-clean in the sense that they are a sum of a nilpotent and an unique idempotent. In fact, we succeeded to prove that these two classes of rings can completely be characterized in terms of already well-studied and fully described sorts of rings. |
| Author | Moussavi, A. Hasanzadeh, O. Danchev, P. Javan, A. |
| Author_xml | – sequence: 1 givenname: P. surname: Danchev fullname: Danchev, P. email: danchev@math.bas.bg, pvdanchev@yahoo.com organization: Institute of Mathematics and Informatics, Bulgarian Academy of Sciences – sequence: 2 givenname: O. surname: Hasanzadeh fullname: Hasanzadeh, O. email: o.hasanzade@modares.ac.ir, hasanzadeomiid@gmail.com organization: Department of Mathematics, Tarbiat Modares University – sequence: 3 givenname: A. surname: Javan fullname: Javan, A. email: a.darajavan@modares.ac.ir, a.darajavan@gmail.com organization: Department of Mathematics, Tarbiat Modares University – sequence: 4 givenname: A. surname: Moussavi fullname: Moussavi, A. email: moussavi.a@modares.ac.ir, moussavi.a@gmail.com organization: Department of Mathematics, Tarbiat Modares University |
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| Keywords | strongly nil-clean element (ring) uniquely clean element (ring) nil-clean element (ring) uniquely nil-clean element (ring) |
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| Title | Rings Whose Non-Invertible Elements Are Strongly Nil-Clean |
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