Linear maps preserving Drazin inverses of matrices over local rings


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

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

  • 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" >RR be a local ring and suppose that there exists a∈F∗" role="presentation" >aFaF such that a6≠1" role="presentation" >a61a61; also let T:Mn(R)→Mm(R)" role="presentation" >T:Mn(R)Mm(R)T:Mn(R)Mm(R) be a linear map preserving Drazin inverses. Then we prove that T=0" role="presentation" >T=0T=0 or n=m" role="presentation" >n=mn=m and T" role="presentation" >TT preserves idempotents. We thereby determine the form of linear maps from Mn(R)" role="presentation" >Mn(R)Mn(R) to Mm(R)" role="presentation" >Mm(R)Mm(R) preserving Drazin inverses of matrices.