4 papers
Strong truncations and Maximal Ideal Principles
Karim Boulabiar, Mohamed Habibi
We compare two existence principles for maximal ideals, a classical one for vector lattices with a strong unit and a second, newly introduced one for vector lattices with a strong…
Order-to-ring ideals via submultiplicative lattice seminorms in lattice-ordered algebras
Karim Boulabiar, Rania Souissi
This paper characterizes lattice-ordered algebras with the order-to-ring ideal property, i.e., those in which every order ideal is a ring ideal. Our main result shows that an Archi…
Best approximation from the positive cone of an inner product lattice
Marouen Abdouli, Karim Boulabiar
Let be a directed (i.e., positively generated) ordered vector space endowed with an inner product. In this note, we prove that the following statements are equivalent: i) i…
Intermediate algebras in Archimedean semiprime f-algebras
Karim Boulabiar
We introduce the notion of bounded quasi-inversion closed semiprime f-algebras and we prove that, if A is such an algebra, then any intermediate algebra in A is an order ideal of A…