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oai:ebyu-rdlopen.rawdatalibrary.net:ebyu/112902026-10-18T20:41:33Zopenairedrivercom_ebyu_10000col_ebyu_10001

A generalization of the generalized Drazin inverse in ringsTien, Nguyen QuocKoşan, M. TamerQuynh, Truong CongÖzdin, TufanDrazin inverseEP-elementgeneralized Drazin inverseJacobson radicalnilpotent elementQuasi-nilpotent elementquasi-polar elementspectral idempotentThe notions of (quasi-) polarity and (generalized) Drazin invertibility of an element a in a ring R, defined upon the set of (quasi-) nilpotent elements, are extended by using the set ∇(R) = {a ∈ R : 1 − au is unit in R for all unit u ∈ R with ua = au}. This set is adapted from the set ∆(R), the largest Jacobson radical subring of R closed by multiplication by units. Uniqueness of the spectral idempotent usually associated to (quasi-) polar decompositions remains, and can be defined by minimal properties. This leads to the definition of a unique Drazin-type inverse for a wider collection of decompositions, encompassing the quasi-polar decompositions. © World Scientific Publishing Company.World Scientific2025Articlehttps://rdlopen.rawdatalibrary.net/r/ebyu/11290https://doi.org/10.1142/s02194988275000710219-4988enJournal of Algebra and its Applicationsinfo:eu-repo/semantics/openAccessinfo:eu-repo/semantics/articlehttps://ebyu-rdlopen.rawdatalibrary.net/tr/items/ebyu/11290