Cancellation of projective modules over regular rings with comparability

P. Ara, K. C. O'Meara, D. V. Tyukavkin

Research output: Contribution to journalArticleResearchpeer-review

36 Citations (Scopus)


This paper answers, in the negative, Open Problem 4 in Goodearl's book on von Neumann regular rings: a directly finite regular ring R with s-comparability is constructed which is not unit-regular. It is shown, however, that the behaviour of these rings R is still quite good. They have cancellation of small projective modules and, in particular, their stable range is at most 2.
Original languageEnglish
Pages (from-to)19-38
JournalJournal of Pure and Applied Algebra
Issue number1
Publication statusPublished - 26 Feb 1996


  • Hermite ring
  • s-comparability
  • Stable range
  • Unit-regular ring
  • Von Neumann regular ring


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