| Autor: |
Rani Goyal, Dimple, Khurana, Anjana, Khurana, Dinesh |
| Předmět: |
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| Zdroj: |
Journal of Algebra & Its Applications; Jul2024, Vol. 23 Issue 8, p1-8, 8p |
| Abstrakt: |
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] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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