Drazin inverse and generalization of core-nilpotent decomposition

Savitha Varkady, Umashankara Kelathaya, Manjunatha Prasad Karantha

Research output: Contribution to journalArticlepeer-review


The Drazin inverse is connected with the notion of index and core-nilpotent decomposition whenever it is discussed in the context of ring of matrices over complex field. In the absence of Drazin inverse for a given element from an arbitrary associative ring (not necessarily with unity), in this paper, the notion of right (left) core-nilpotent decomposition has been introduced and established its relations with right (left) π-regular property. In fact, the class of such decomposition has been characterized. In case of regular ring, observed that an element is right (left) π-regular if and only if it has a right (left) core-nilpotent decomposition. In the process, several properties of sharp order in an associative ring are studied and with the help of the same, new characterizations of Drazin inverse over an associative ring are obtained and the relation between core-nilpotent decomposition and the Drazin inverse is obtained.

Original languageEnglish
Article number2450041
JournalJournal of Algebra and Its Applications
Publication statusAccepted/In press - 2022

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Applied Mathematics


Dive into the research topics of 'Drazin inverse and generalization of core-nilpotent decomposition'. Together they form a unique fingerprint.

Cite this