Geodesic
Sharp partial order of core-nilpotent endomorphisms
Filomat, Tome 37 (2023) no. 10, p. 3167

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DOI

The aim of this work is to offer a definition of the sharp partial order for the set of Core-Nilpotent endomorphisms. The main properties of this partial order are studied, generalizing the notion of sharp partial order of finite square matrices. In order to do so, the structure of the set of {1}-commuting inverses of a Core-Nilpotent endomorphism is described, and in particular, the structure of the set of {1}-commuting inverses of finite square matrices with entries in an arbitrary field is determined and an algorithm for its computation is provided.
DOI : 10.2298/FIL2310167A
Classification : 15A09, 15A03, 15A04
Keywords: Sharp Partial order, Core-Nilpotent Endomorphism, {1}−commuting inverses, Square Matrices 
Diego Alba Alonso. Sharp partial order of core-nilpotent endomorphisms. Filomat, Tome 37 (2023) no. 10, p. 3167 . doi: 10.2298/FIL2310167A
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     author = {Diego Alba Alonso},
     title = {Sharp partial order of core-nilpotent endomorphisms},
     journal = {Filomat},
     pages = {3167 },
     year = {2023},
     volume = {37},
     number = {10},
     doi = {10.2298/FIL2310167A},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2310167A/}
}
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