Linear maps preserving Drazin inverses of matrices over local rings

CHEN, HUANYIN; ÇALCI, TUĞÇE; HALICIOĞLU, SAİT; Shile, Guo

doi:10.33044/revuma.1858

Linear maps preserving Drazin inverses of matrices over local rings

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CHEN H., ÇALCI T., HALICIOĞLU S., Shile G.

REVISTA DE LA UNION MATEMATICA ARGENTINA, vol.62, no.2, pp.415-422, 2021 (SCI-Expanded)

Publication Type: Article / Article
Volume: 62 Issue: 2
Publication Date: 2021
Doi Number: 10.33044/revuma.1858
Journal Name: REVISTA DE LA UNION MATEMATICA ARGENTINA
Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, Directory of Open Access Journals, DIALNET
Page Numbers: pp.415-422
Keywords: Linear map, Drazin inverse, local ring, SUM, IDEMPOTENCE, MODULES
Ankara University Affiliated: Yes

Abstract

Let R" role="presentation" >R $R$ be a local ring and suppose that there exists a∈F∗" role="presentation" >a∈F∗ $a \in F^{*}$ such that a6≠1" role="presentation" >a6≠1 $a^{6} \neq 1$ ; also let T:Mn(R)→Mm(R)" role="presentation" >T:Mn(R)→Mm(R) $T : M_{n} (R) \to M_{m} (R)$ be a linear map preserving Drazin inverses. Then we prove that T=0" role="presentation" >T=0 $T = 0$ or n=m" role="presentation" >n=m $n = m$ and T" role="presentation" >T $T$ preserves idempotents. We thereby determine the form of linear maps from Mn(R)" role="presentation" >Mn(R) $M_{n} (R)$ to Mm(R)" role="presentation" >Mm(R) $M_{m} (R)$ preserving Drazin inverses of matrices.