Certain strongly clean matrices over local rings

ÇALCI T., Chen H.

TURKISH JOURNAL OF MATHEMATICS, vol.42, no.5, pp.2296-2303, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 42 Issue: 5
  • Publication Date: 2018
  • Doi Number: 10.3906/mat-1802-10
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.2296-2303
  • Keywords: Matrix ring, strongly clean matrix, quasipolar matrix, PSEUDO DRAZIN INVERSE, BANACH-ALGEBRAS, ELEMENTS, PROPERTY
  • Ankara University Affiliated: Yes

Abstract

We are concerned about various strongly clean properties of a kind of matrix subrings L-(s) (R) over a local ring R. Let R be a local ring, and let s is an element of C(R). We prove that A is an element of L-(s) (R) is strongly clean if and only if A or I-2 - A is invertible, or A is similar to a diagonal matrix in L-(s) (R). Furthermore, we prove that A is an element of L-(s) (R) is quasipolar A if and only if A is an element of GL(2) (R) or A is an element of L-(s)(R)(qnil) or A is similar to a diagonal matrix in