Strongly J-Clean Rings with Involutions

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

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.
Original languageEnglish
Title of host publicationRing Theory And Its Applications: Ring Theory Session In Honor Of T.y. Lam On His 70th Birthday
EditorsDV Huynh, SK Jain, SR LopezPermouth, ST Rizvi, CS Roman
PublisherAmer Mathematical Soc
Pages33-+
Number of pages2
Volume609
ISBN (Print)978-0-8218-8797-4
DOIs
Publication statusPublished - 2014
Event31st Ohio State-Denison Mathematics Conference - Columbus
Duration: 25 May 201227 May 2012

Publication series

NameContemporary Mathematics

Conference

Conference31st Ohio State-Denison Mathematics Conference
CityColumbus
Period25/05/1227/05/12

Keywords

  • Strongly J-clean rings
  • Strongly *-clean rings
  • Uniquely clean rings

Fingerprint

Dive into the research topics of 'Strongly J-Clean Rings with Involutions'. Together they form a unique fingerprint.

Cite this