Representations of the Drazin inverse involving idempotents in a ring
Huihui Zhu, Jianlong Chen
TL;DR
This paper develops formulas for the Drazin inverse of differences and products of idempotents in rings, extending known results from bounded linear operators in Banach spaces to a more general algebraic setting.
Contribution
It introduces new formulas for the Drazin inverse involving idempotents in rings, generalizing existing operator results to ring theory.
Findings
Formulas for the Drazin inverse of differences of idempotents
Formulas for the Drazin inverse of products of idempotents
Extension of operator results to ring context
Abstract
We present some formulae for the Drazin inverse of difference and product of idempotents in a ring. A number of results of bounded linear operators in Banach spaces are extended to the ring case.
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Taxonomy
TopicsMatrix Theory and Algorithms · Advanced Topics in Algebra · Algebraic and Geometric Analysis