A Note on Extensions of Bear and P.p.-rings
N. J. Groenewald (1983)
Publications de l'Institut Mathématique
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A Note on Extensions of Bear and P.p.-rings
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A lattice-ordered ring is called an if each of its order ideals is a ring ideal. Generalizing earlier work of Basly and Triki, OIRI-rings are characterized as those -rings such that is contained in an -ring with an identity element that is a strong order unit for some nil -ideal of . In particular, if denotes the set of nilpotent elements of the -ring , then is an OIRI-ring if and only if is contained in an -ring with an identity element that is a strong order unit. ...