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On Strongly Jn-Clean Rings.
- Source :
-
Bulletin of the Iranian Mathematical Society . Apr2019, Vol. 45 Issue 2, p627-639. 13p. - Publication Year :
- 2019
-
Abstract
- A ring R is said to be strongly J n -clean if n is the least positive integer such that every element a is strongly J n -clean, that is, there exists an idempotent e such that e a = a e , a - e is a unit and e a n is in the Jacobson radical J(R). It is proved that strongly J n -clean ring is a strongly clean ring with stable range one. If R is an abelian ring (a ring in which all idempotents are central), then R is strongly J n -clean if and only if R / J(R) is strongly π -regular and idempotents lift modulo J(R). Some examples and basic properties of these rings are studied. Some criterions in terms of solvability of the characteristic equation are obtained for such a 2 × 2 matrix to be strongly J 2 -clean. [ABSTRACT FROM AUTHOR]
- Subjects :
- *JACOBSON radical
*IDEMPOTENTS
*ASSOCIATIVE rings
Subjects
Details
- Language :
- English
- ISSN :
- 10186301
- Volume :
- 45
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Bulletin of the Iranian Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 135891647
- Full Text :
- https://doi.org/10.1007/s41980-018-0154-2