Arens regularity of lattice-ordered rings

Karim Boulabiar; Jamel Jabeur

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Yosida-Fukamiya's theorem for ƒ-rings

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When is every order ideal a ring ideal?

Melvin Henriksen, Suzanne Larson, Frank A. Smith (1991)

Commentationes Mathematicae Universitatis Carolinae

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A lattice-ordered ring $ℝ$ 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 $f$ -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. ...