Drazin inverse and generalization of core-nilpotent decomposition. (English) Zbl 1529.15004
The authors explore the connection between the Drazin inverse and the core-nilpotent decomposition. The Drazin inverse does not exist in cases where a given element lacks strong \(\pi\)-regularity. Consequently, it becomes interesting to explore the generalization of core-nilpotent decomposition and its association with any extended form of the Drazin inverse, such as the right (left) \(\pi\)-inverse. The paper introduces novel characterizations of the Drazin inverse and its correlation with core-nilpotent decomposition, employing sharp order as a defining criterion.
Reviewer: Mohammad Sal Moslehian (Mashhad)
MSC:
| 15A09 | Theory of matrix inversion and generalized inverses |
| 16E50 | von Neumann regular rings and generalizations (associative algebraic aspects) |
| 06A06 | Partial orders, general |
Keywords:
generalized inverse; Drazin inverse; minus partial order; sharp order; core-nilpotent decompositionReferences:
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