Quasi-implication algebras

Ivan Chajda; Kamil Dušek

Displaying similar documents to “Quasi-implication algebras”

Sets and Posets with Inversions

Árpád Száz (2011)

Publications de l'Institut Mathématique

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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...

Some remarks on certain classes of semilattices.

Murty, P.V.Ramana, Murty, M.Krishna (1982)

International Journal of Mathematics and Mathematical Sciences

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Reflexive and antisymmetric relations and their systems

Jiří Rachůnek (1981)

Czechoslovak Mathematical Journal

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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...

Triple construction of semilattices with $1$ admitting neutral $p$ -closure operators

P.V. Ramana Murty, V. Raman (1982)

Mathematica Slovaca

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Hilbert algebras as implicative partial semilattices

Jānis Cīrulis (2007)

Open Mathematics

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The infimum of elements a and b of a Hilbert algebra are said to be the compatible meet of a and b, if the elements a and b are compatible in a certain strict sense. The subject of the paper will be Hilbert algebras equipped with the compatible meet operation, which normally is partial. A partial lower semilattice is shown to be a reduct of such an expanded Hilbert algebra i ?both algebras have the same ?lters.An expanded Hilbert algebra is actually an implicative partial semilattice...

Adjoint Semilattice and Minimal Brouwerian Extensions of a Hilbert Algebra

Jānis Cīrulis (2012)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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Let $A : = (A, \to, 1)$ be a Hilbert algebra. The monoid of all unary operations on $A$ generated by operations $α_{p} : x \mapsto (p \to x)$ , which is actually an upper semilattice w.r.t. the pointwise ordering, is called the adjoint semilattice of $A$ . This semilattice is isomorphic to the semilattice of finitely generated filters of $A$ , it is subtractive (i.e., dually implicative), and its ideal lattice is isomorphic to the filter lattice of $A$ . Moreover, the order dual of the adjoint semilattice is a minimal Brouwerian extension of...