Almost unit-clean rings

Chen H., KÖSE H., Kurtulmaz Y.

Mathematical Reports, cilt.21, sa.1, ss.113-121, 2019 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 21 Sayı: 1
  • Basım Tarihi: 2019
  • Dergi Adı: Mathematical Reports
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.113-121
  • Anahtar Kelimeler: Almost unit-clean ring, Elementary divisor ring, Strongly π-regular ring
  • Ankara Üniversitesi Adresli: Evet

Özet

A ring R is almost unit-clean provided that every element in R is equivalent to the sum of an idempotent and a regular element. We prove that every ring in which every zero-divisor is strongly π-regular is almost unit-clean and every matrix ring of elementary divisor domains is almost unit-clean. Furthermore, it is shown that the trivial extension R(M) of a commutative ring R and an R-module M is almost unit-clean if and only if each x ∈ R can be written in the form ux = r + e where u ∈ U(R), r ∈ R − (Z(R) ∪ Z(M)) and e ∈ Id(R). We thereby construct many examples of such rings.