When is Every Order Ideal a Ring Ideal?

Authors

Melvin Henriksen, Harvey Mudd CollegeFollow
Suzanne Larson, Loyola Marymount University
Frank A. Smith, Kent State UniversityFollow

Document Type

Article

Department

Mathematics (HMC)

Publication Date

1991

Abstract

A lattice-ordered ring ℝ 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 ℝ such that ℝ/I is contained in an f-ring with an identity element that is a strong order unit for some nil l-ideal I of ℝ. In particular, if P(ℝ) denotes the set of nilpotent elements of the f-ring ℝ, then ℝ is an OIRI-ring if and only if ℝ/P(ℝ) is contained in an f-ring with an identity element that is a strong order unit.

Comments

Previously linked to as: http://ccdl.libraries.claremont.edu/u?/irw,434

Article can also be found at http://dml.cz/dmlcz/116985

Rights Information

© 1991 Charles University in Prague

Terms of Use & License Information

Terms of Use for work posted in Scholarship@Claremont.

Recommended Citation

Henriksen, M., S. Larson, and F. A. Smith. "When is every order ideal a ring ideal?" Commentationes Mathematicae Universitatis Carolinae 32.3 (1991): 411-416.