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

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