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- Title
Strongly 2-nil-clean rings.
- Authors
Chen, Huanyin; Sheibani, Marjan
- Abstract
A ring is strongly 2-nil-clean if every element in is the sum of two idempotents and a nilpotent that commute. Fundamental properties of such rings are obtained. We prove that a ring is strongly 2-nil-clean if and only if for all , is nilpotent, if and only if for all , is strongly nil-clean, if and only if every element in is the sum of a tripotent and a nilpotent that commute. Furthermore, we prove that a ring is strongly 2-nil-clean if and only if is tripotent and is nil, if and only if or , where is a Boolean ring and is nil; is a Yaqub ring and is nil. Strongly 2-nil-clean group algebras are investigated as well.
- Subjects
RING theory; IDEMPOTENTS; BOOLEAN rings; GROUP theory; NILPOTENT groups
- Publication
Journal of Algebra & Its Applications, 2017, Vol 16, Issue 9, p-1
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S021949881750178X