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

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

REVISTA DE LA UNION MATEMATICA ARGENTINA, cilt.62, sa.2, ss.415-422, 2021 (SCI-Expanded, Scopus)

Yayın Türü: Makale / Tam Makale
Cilt numarası: 62 Sayı: 2
Basım Tarihi: 2021
Doi Numarası: 10.33044/revuma.1858
Dergi Adı: REVISTA DE LA UNION MATEMATICA ARGENTINA
Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, Directory of Open Access Journals, DIALNET
Sayfa Sayıları: ss.415-422
Anahtar Kelimeler: Linear map, Drazin inverse, local ring, SUM, IDEMPOTENCE, MODULES
Ankara Üniversitesi Adresli: Evet

Özet

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.