Displaying similar documents to “An introduction to the theory of H v -semilattices.”

Distributive multisemilattices

Arthur Knoebel, Anna Romanowska

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A distributive multisemilattice of type n is an algebra with a family of n binary semilattice operations on a common carrier that are mutually distributive. This concept for n=2 comprises the distributive bisemilattices (or quasilattices), of which distributive lattices and semilattices with duplicated operations are the best known examples. Multisemilattices need not satisfy the absorption law, which holds in all lattices.Kalman has exhibited a subdirectly irreducible distributive bisemilattice...

Relative annihilator-preserving congruence relations and relative annihilator-preserving homomorphisms in bounded distributive semilattices

Sergio A. Celani (2015)

Open Mathematics

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In this paper we shall study a notion of relative annihilator-preserving congruence relation and relative annihilator-preserving homomorphism in the class of bounded distributive semilattices. We shall give a topological characterization of this class of semilattice homomorphisms. We shall prove that the semilattice congruences that are associated with filters are exactly the relative annihilator-preserving congruence relations.

Means on scattered compacta

T. Banakh, R. Bonnet, W. Kubis (2014)

Topological Algebra and its Applications

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We prove that a separable Hausdor_ topological space X containing a cocountable subset homeomorphic to [0, ω1] admits no separately continuous mean operation and no diagonally continuous n-mean for n ≥ 2.

On JP-semilattices of Begum and Noor

Jānis Cīrulis (2013)

Mathematica Bohemica

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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...

On unique factorization semilattices

Pedro V. Silva (2000)

Discussiones Mathematicae - General Algebra and Applications

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The class of unique factorization semilattices (UFSs) contains important examples of semilattices such as free semilattices and the semilattices of idempotents of free inverse monoids. Their structural properties allow an efficient study, among other things, of their principal ideals. A general construction of UFSs from arbitrary posets is presented and some categorical properties are derived. The problem of embedding arbitrary semilattices into UFSs is considered and complete characterizations...