TY - JOUR

T1 - Drazin inverse and generalization of core-nilpotent decomposition

AU - Varkady, Savitha

AU - Kelathaya, Umashankara

AU - Karantha, Manjunatha Prasad

N1 - Publisher Copyright:
© 2024 World Scientific Publishing Company.

PY - 2022

Y1 - 2022

N2 - 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.

AB - 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.

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U2 - 10.1142/S0219498824500415

DO - 10.1142/S0219498824500415

M3 - Article

AN - SCOPUS:85143843880

SN - 0219-4988

JO - Journal of Algebra and Its Applications

JF - Journal of Algebra and Its Applications

M1 - 2450041

ER -