Strongly J-Clean Rings with Involutions
31st Ohio State-Denison Mathematics Conference, Ohio, Amerika Birleşik Devletleri, 25 - 27 Mayıs 2012, cilt.609, ss.33-34, (Tam Metin Bildiri)
- Yayın Türü: Bildiri / Tam Metin Bildiri
- Cilt numarası: 609
- Doi Numarası: 10.1090/conm/609/12122
- Basıldığı Şehir: Ohio
- Basıldığı Ülke: Amerika Birleşik Devletleri
- Sayfa Sayıları: ss.33-34
- Hacettepe Üniversitesi Adresli: Evet
Özet
A *-ring R is strongly J-*-clean provided that for any a is an element of R, there exists a projection e is an element of R such that a - e is an element of J(R) and ae = ea where J(R) is the Jacobson radical of R. Here it is proved that a *-ring R is strongly J-*-clean, if and only if R is uniquely clean and strongly *-clean, if and only if for any a is an element of R, there exists a unique projection e is an element of R such that a - e is invertible and ae = ea. As a consequence, strong J-cleanness and uniquely strong cleanness coincide with each other under any involutions.