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α -ideals in 0 -distributive posets

Khalid A. Mokbel (2015)

Mathematica Bohemica

The concept of α -ideals in posets is introduced. Several properties of α -ideals in 0 -distributive posets are studied. Characterization of prime ideals to be α -ideals in 0 -distributive posets is obtained in terms of minimality of ideals. Further, it is proved that if a prime ideal I of a 0 -distributive poset is non-dense, then I is an α -ideal. Moreover, it is shown that the set of all α -ideals α Id ( P ) of a poset P with 0 forms a complete lattice. A result analogous to separation theorem for finite 0 -distributive...

δ -ideals in pseudo-complemented distributive lattices

M. Sambasiva Rao (2012)

Archivum Mathematicum

The concept of δ -ideals is introduced in a pseudo-complemented distributive lattice and some properties of these ideals are studied. Stone lattices are characterized in terms of δ -ideals. A set of equivalent conditions is obtained to characterize a Boolean algebra in terms of δ -ideals. Finally, some properties of δ -ideals are studied with respect to homomorphisms and filter congruences.

κ-compactness, extent and the Lindelöf number in LOTS

David Buhagiar, Emmanuel Chetcuti, Hans Weber (2014)

Open Mathematics

We study the behaviour of ℵ-compactness, extent and Lindelöf number in lexicographic products of linearly ordered spaces. It is seen, in particular, that for the case that all spaces are bounded all these properties behave very well when taking lexicographic products. We also give characterizations of these notions for generalized ordered spaces.

λ -lattices

Václav Snášel (1997)

Mathematica Bohemica

In this paper, we generalize the notion of supremum and infimum in a poset.

σ -interpolation lattice-ordered groups

Michael R. Darnel (2000)

Czechoslovak Mathematical Journal

In [1], Jakubík showed that the class of σ -interpolation lattice-ordered groups forms a radical class, but left open the question of whether the class forms a torsion class. In this paper, we show that this class does indeed form a torsion class.

Σ -isomorphic algebraic structures

Ivan Chajda, Petr Emanovský (1995)

Mathematica Bohemica

For an algebraic structure = ( A , F , R ) or type and a set Σ of open formulas of the first order language L ( ) we introduce the concept of Σ -closed subsets of . The set ℂ Σ ( ) of all Σ -closed subsets forms a complete lattice. Algebraic structures , of type are called Σ -isomorphic if ℂ Σ ( ) ≅ ℂ Σ ( ) . Examples of such Σ -closed subsets are e.g. subalgebras of an algebra, ideals of a ring, ideals of a lattice, convex subsets of an ordered or quasiordered set etc. We study Σ -isomorphic algebraic structures in dependence on the...

σ-Entangled linear orders and narrowness of products of Boolean algebras

Saharon Shelah (1997)

Fundamenta Mathematicae

We investigate σ-entangled linear orders and narrowness of Boolean algebras. We show existence of σ-entangled linear orders in many cardinals, and we build Boolean algebras with neither large chains nor large pies. We study the behavior of these notions in ultraproducts.

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