Strongly J-Clean Rings with Involutions


CHEN H., HARMANCI A., ÖZCAN A. Ç.

31st Ohio State-Denison Mathematics Conference, Ohio, United States Of America, 25 - 27 May 2012, vol.609, pp.33-34 identifier

  • Publication Type: Conference Paper / Full Text
  • Volume: 609
  • Doi Number: 10.1090/conm/609/12122
  • City: Ohio
  • Country: United States Of America
  • Page Numbers: pp.33-34
  • Hacettepe University Affiliated: Yes

Abstract

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.