Distributive associative near lattices
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Dietmar Schweigert (1985)
Mathematica Slovaca
Henri Mühle (2021)
Mathematica Bohemica
Distributive lattices form an important, well-behaved class of lattices. They are instances of two larger classes of lattices: congruence-uniform and semidistributive lattices. Congruence-uniform lattices allow for a remarkable second order of their elements: the core label order; semidistributive lattices naturally possess an associated flag simplicial complex: the canonical join complex. In this article we present a characterization of finite distributive lattices in terms of the core label order...
Heleyová, Z. (1995)
Acta Mathematica Universitatis Comenianae. New Series
Joanna Grygiel (2004)
Discussiones Mathematicae - General Algebra and Applications
We present a construction of finite distributive lattices with a given skeleton. In the case of an H-irreducible skeleton K the construction provides all finite distributive lattices based on K, in particular the minimal one.
Joel Berman (1977)
Aequationes mathematicae
Joel Berman (1977)
Aequationes mathematicae
Arthur Knoebel, Anna Romanowska (1991)
Josef Niederle (2006)
Discussiones Mathematicae - General Algebra and Applications
Brouwerian ordered sets generalize Brouwerian lattices. The aim of this paper is to characterize (α)-complete Brouwerian ordered sets in a manner similar to that used previously for pseudocomplemented, Stone, Boolean and distributive ordered sets. The sublattice (G(P)) in the Dedekind-Mac~Neille completion (DM(P)) of an ordered set (P) generated by (P) is said to be the characteristic lattice of (P). We can define a stronger notion of Brouwerianicity by demanding that both (P) and (G(P)) be Brouwerian....
Waphare, B.N., Joshi, V.V. (2004)
Acta Mathematica Universitatis Comenianae. New Series
R. Hickman, G. Monro (1984)
Fundamenta Mathematicae
S.P. Avann (1961)
Mathematische Zeitschrift
Rai, Shashirekha B. (2008)
Acta Mathematica Universitatis Comenianae. New Series
Domenico Boccioni (1971)
Rendiconti del Seminario Matematico della Università di Padova
Mária Jakubíková (1975)
Matematický časopis
Serra Alves, Carlos (1995)
Portugaliae Mathematica
Ladislav Beran (1987)
Commentationes Mathematicae Universitatis Carolinae
Ján Jakubík (1972)
Czechoslovak Mathematical Journal
Ivan Chajda (2005)
Discussiones Mathematicae - General Algebra and Applications
We present a simple condition under which a bounded lattice L with sectionally antitone involutions becomes an MV-algebra. In thiscase, L is distributive. However, we get a criterion characterizingdistributivity of L in terms of antitone involutions only.
Ján Jakubík (1982)
Czechoslovak Mathematical Journal
Daniel Ruiz-Aguilera, Joan Torrens (2006)
Kybernetika
This paper deals with implications defined from disjunctive uninorms by the expression where is a strong negation. The main goal is to solve the functional equation derived from the distributivity condition of these implications over conjunctive and disjunctive uninorms. Special cases are considered when the conjunctive and disjunctive uninorm are a -norm or a -conorm respectively. The obtained results show a lot of new solutions generalyzing those obtained in previous works when the implications...