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

Atıf İçin Kopyala

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

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

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.