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Products in almost f -algebras

Karim Boulabiar — 2000

Commentationes Mathematicae Universitatis Carolinae

Let A be a uniformly complete almost f -algebra and a natural number p ∈ { 3 , 4 , ⋯ } . Then Π p ( A ) = { a 1 ⋯ a p ; a k ∈ A , k = 1 , ⋯ , p } is a uniformly complete semiprime f -algebra under the ordering and multiplication inherited from A with Σ p ( A ) = { a p ; 0 ≤ a ∈ A } as positive cone.

Arens regularity of lattice-ordered rings

Karim Boulabiar;  Jamel Jabeur — 2010

Annales de la faculté des sciences de Toulouse Mathématiques

This work discusses the problem of Arens regularity of a lattice-ordered ring. In this prospect, a counterexample is furnished to show that without extra conditions, a lattice-ordered ring need not be Arens regular. However, as shown in this paper, it turns out that any f -ring in the sense of Birkhoff and Pierce is Arens regular. This result is then used and extended to the more general setting of almost f -rings introduced again by Birkhoff.

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