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Strongly π-regular elements and Drazin inverses.
- Source :
- Journal of Algebra & Its Applications; Jul2024, Vol. 23 Issue 8, p1-8, 8p
- Publication Year :
- 2024
-
Abstract
- We find an expression for the Drazin inverse of a strongly π -regular element a in the form a i x j when a n = a n + k x for some nonnegative integer n and positive integer k. This extends the result by Azumaya, which is the case when n = 1 and k = 1 , and a result by Drazin, which is the case when n is arbitrary and k = 1. We give new proofs of several results in the literature. For instance, we give an easy proof of the result that for two commuting Drazin invertible elements a , b of R , then a + b is Drazin invertible if and only if so is 1 + a D b , where a D is the Drazin inverse of a. Our proof is akin to the case when a and b are invertible. [ABSTRACT FROM AUTHOR]
- Subjects :
- LITERATURE
Subjects
Details
- Language :
- English
- ISSN :
- 02194988
- Volume :
- 23
- Issue :
- 8
- Database :
- Complementary Index
- Journal :
- Journal of Algebra & Its Applications
- Publication Type :
- Academic Journal
- Accession number :
- 178020467
- Full Text :
- https://doi.org/10.1142/S0219498825500434