EuDML | Browse

In this paper we prove that the collection of all weakly distributive lattice ordered groups is a radical class and that it fails to be a torsion class.

Weakly associative lattice rings

Dana Šalounová (2000)

Acta Mathematica et Informatica Universitatis Ostraviensis

Weakly prime and prime fuzzy ideals in ordered semigroups.

Kehayopulu, Niovi (2007)

Lobachevskii Journal of Mathematics

When is a total ordering of a semigroup a well-ordering?.

G. Revész (1990)

Semigroup forum

When is every order ideal a ring ideal?

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

Commentationes Mathematicae Universitatis Carolinae

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....

When $Min {(G)}^{- 1}$ has a clopen $π$ -base

Ramiro Lafuente-Rodriguez, Warren Wm. McGovern (2021)

Mathematica Bohemica

It is our aim to contribute to the flourishing collection of knowledge centered on the space of minimal prime subgroups of a given lattice-ordered group. Specifically, we are interested in the inverse topology. In general, this space is compact and $T_{1}$ , but need not be Hausdorff. In 2006, W. Wm. McGovern showed that this space is a boolean space (i.e. a compact zero-dimensional and Hausdorff space) if and only if the $l$ -group in question is weakly complemented. A slightly weaker topological property...