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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...

When spectra of lattices of $z$ -ideals are Stone-Čech compactifications

Themba Dube (2017)

Mathematica Bohemica

Let $X$ be a completely regular Hausdorff space and, as usual, let $C (X)$ denote the ring of real-valued continuous functions on $X$ . The lattice of $z$ -ideals of $C (X)$ has been shown by Martínez and Zenk (2005) to be a frame. We show that the spectrum of this lattice is (homeomorphic to) $β X$ precisely when $X$ is a $P$ -space. This we actually show to be true not only in spaces, but in locales as well. Recall that an ideal of a commutative ring is called a $d$ -ideal if whenever two elements have the same annihilator and...

Displaying 41 – 51 of 51

When is every order ideal a ring ideal?

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

When spectra of lattices of $z$ -ideals are Stone-Čech compactifications

Where the typical set partitions meet and join.

Which countable ordered sets have a dense linear extension?

Words avoiding a reflexive acyclic relation.

Wreath Products and Equations in Semigroups - in Russisch

Wreath products and universal equivalence.

Wreath products of ordered semigroups.

Wreath products of ordered semigroups, II. Inverse ordered wreath products.

Wreath products of permutation classes.

Currently displaying 41 – 51 of 51