All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 5 Next

Displaying 81 – 100 of 195

Showing per page

Independent axiom systems for nearlattices

João Araújo, Michael Kinyon (2011)

Czechoslovak Mathematical Journal

A nearlattice is a join semilattice such that every principal filter is a lattice with respect to the induced order. Hickman and later Chajda et al independently showed that nearlattices can be treated as varieties of algebras with a ternary operation satisfying certain axioms. Our main result is that the variety of nearlattices is 2 -based, and we exhibit an explicit system of two independent identities. We also show that the original axiom systems of Hickman as well as that of Chajda et al are...

Join-semilattices with two-dimensional congruence amalgamation

Friedrich Wehrung (2002)

Colloquium Mathematicae

We say that a ⟨∨,0⟩-semilattice S is conditionally co-Brouwerian if (1) for all nonempty subsets X and Y of S such that X ≤ Y (i.e. x ≤ y for all ⟨x,y⟩ ∈ X × Y), there exists z ∈ S such that X ≤ z ≤ Y, and (2) for every subset Z of S and all a, b ∈ S, if a ≤ b ∨ z for all z ∈ Z, then there exists c ∈ S such that a ≤ b ∨ c and c ≤ Z. By restricting this definition to subsets X, Y, and Z of less than κ elements, for an infinite cardinal κ, we obtain the definition of a conditionally κ-co-Brouwerian...

Lattices and semilattices having an antitone involution in every upper interval

Ivan Chajda (2003)

Commentationes Mathematicae Universitatis Carolinae

We study ∨ -semilattices and lattices with the greatest element 1 where every interval [p,1] is a lattice with an antitone involution. We characterize these semilattices by means of an induced binary operation, the so called sectionally antitone involution. This characterization is done by means of identities, thus the classes of these semilattices or lattices form varieties. The congruence properties of these varieties are investigated.

Lattices of Scott-closed sets

Weng Kin Ho, Dong Sheng Zhao (2009)

Commentationes Mathematicae Universitatis Carolinae

A dcpo P is continuous if and only if the lattice C ( P ) of all Scott-closed subsets of P is completely distributive. However, in the case where P is a non-continuous dcpo, little is known about the order structure of C ( P ) . In this paper, we study the order-theoretic properties of C ( P ) for general dcpo’s P . The main results are: (i) every C ( P ) is C-continuous; (ii) a complete lattice L is isomorphic to C ( P ) for a complete semilattice P if and only if L is weak-stably C-algebraic; (iii) for any two complete semilattices...

Monadic quasi-modal distributive nearlattices

Ismael Calomino (2023)

Commentationes Mathematicae Universitatis Carolinae

We prove that there is a one to one correspondence between monadic finite quasi-modal operators on a distributive nearlattice and quantifiers on the distributive lattice of its finitely generated filters, extending the results given in ``Calomino I., Celani S., González L. J.: Quasi-modal operators on distributive nearlattices, Rev. Unión Mat. Argent. 61 (2020), 339--352".

Note on α -filters in distributive nearlattices

Ismael Calomino (2019)

Mathematica Bohemica

In this short paper we introduce the notion of α -filter in the class of distributive nearlattices and we prove that the α -filters of a normal distributive nearlattice are strongly connected with the filters of the distributive nearlattice of the annihilators.

On distances and metrics in discrete ordered sets

Stephan Foldes, Sándor Radelecki (2021)

Mathematica Bohemica

Discrete partially ordered sets can be turned into distance spaces in several ways. The distance functions may or may not satisfy the triangle inequality and restrictions of the distance to finite chains may or may not coincide with the natural, difference-of-height distance measured in a chain. It is shown that for semilattices the semimodularity ensures the good behaviour of the distances considered. The Jordan-Dedekind chain condition, which is weaker than semimodularity, is equivalent to the...

On distributive trices

Kiyomitsu Horiuchi, Andreja Tepavčević (2001)

Discussiones Mathematicae - General Algebra and Applications

A triple-semilattice is an algebra with three binary operations, which is a semilattice in respect of each of them. A trice is a triple-semilattice, satisfying so called roundabout absorption laws. In this paper we investigate distributive trices. We prove that the only subdirectly irreducible distributive trices are the trivial one and a two element one. We also discuss finitely generated free distributive trices and prove that a free distributive trice with two generators has 18 elements.

On JP-semilattices of Begum and Noor

Jānis Cīrulis (2013)

Mathematica Bohemica

In recent papers, S. N. Begum and A. S. A. Noor have studied join partial semilattices (JP-semilattices) defined as meet semilattices with an additional partial operation (join) satisfying certain axioms. We show why their axiom system is too weak to be a satisfactory basis for the authors' constructions and proofs, and suggest an additional axiom for these algebras. We also briefly compare axioms of JP-semilattices with those of nearlattices, another kind of meet semilattices with a partial join...

Currently displaying 81 – 100 of 195