Strongly J-Clean Rings with Involutions


CHEN H., HARMANCI A., ÖZCAN A. Ç.

31st Ohio State-Denison Mathematics Conference, Ohio, Amerika Birleşik Devletleri, 25 - 27 Mayıs 2012, cilt.609, ss.33-34 identifier

  • 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.