On Medium *-Clean Rings
Mediterranean Journal of Mathematics, cilt.16, sa.1, 2019 (SCI-Expanded, Scopus)
- 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.