On Medium *-Clean Rings

Chen H., Abdolyousefi M. S., KÖSE H.

Mediterranean Journal of Mathematics, cilt.16, sa.1, 2019 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 16 Sayı: 1
  • Basım Tarihi: 2019
  • Doi Numarası: 10.1007/s00009-018-1297-3
  • Dergi Adı: Mediterranean Journal of Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: *-clean ring, homomorphic image, Jacobson radical, Projection
  • Ankara Üniversitesi Adresli: Evet

Özet

A *-ring R is called a medium *-clean ring if every element in R is the sum or difference of an element in its Jacobson radical and a projection that commute. We prove that a ring R is medium *-clean if and only if R is strongly *-clean and R / J(R) is a Boolean ring, Z3 or the product of such rings, if and only if R weakly J-*-clean and a2∈ R is uniquely *-clean for all a∈ R, if and only if every idempotent lifts modulo J(R), R is abelian and R / J(R) weakly *-Boolean. A subclass of medium *-clean rings with many nilpotents is thereby characterized.