#### 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.

#### Rights Information

© 1991 Charles University in Prague

#### Terms of Use & License Information

#### 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.

## Comments

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

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