When is Every Order Ideal a Ring Ideal?

Melvin Henriksen, Suzanne Larson, Frank A. Smith

Research output: Contribution to journal › Article › peer-review

Abstract

<p> A lattice-ordered ring &reals; is called an OIRI-ring if each of its order ideals is a ring ideal. Generalizing earlier work of Basly and Triki, OIRI-rings are characterized as those f-rings &reals; such that &reals;/I is contained in an f-ring with an identity element that is a strong order unit for some nil l-ideal I of &reals;. In particular, if P(&reals;) denotes the set of nilpotent elements of the f-ring &reals;, then &reals; is an OIRI-ring if and only if &reals;/P(&reals;) is contained in an f-ring with an identity element that is a strong order unit.</p>
Original languageAmerican English
Pages (from-to)411-416
JournalCommentationes Mathematicae Universitatis Carolinae
Volume32
Issue number3
StatePublished - Jan 1 1991

Keywords

  • f-ring
  • OIRI-ring
  • Strong order unit
  • l-ideal
  • Nilpotent groups
  • Annihilator
  • Order ideal
  • Ring ideal
  • Unitable
  • Vector lattices
  • Archimedian

Disciplines

  • Mathematics
  • Physical Sciences and Mathematics

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