Very clean matrices over local rings

ÜNGÖR B., Chen H., HALICIOĞLU S.

Analele Stiintifice ale Universitatii Al I Cuza din Iasi - Matematica, cilt.63, sa.F3, 2017 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 63 Sayı: F3
  • Basım Tarihi: 2017
  • Dergi Adı: Analele Stiintifice ale Universitatii Al I Cuza din Iasi - Matematica
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: Local ring, Very clean matrix, Very clean ring
  • Ankara Üniversitesi Adresli: Evet

Özet

© 2018, Universitatii Al.I.Cuza din Iasi. All rights reserved.An element a ∈ R is very clean provided that there exists an idempotent e ∈ R such that ae = ea and either a − e or a + e is invertible in R. A ring R is very clean in case every element in R is very clean. We explore the necessary and sufficient conditions under which a triangular 2 × 2 matrix ring over local rings is very clean. The very clean 2 × 2 matrices over commutative local rings are completely determined. Applications to matrices over power series are also obtained.