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Displaying 761 – 780 of 975

The dimension of a variety

Ewa Graczyńska, Dietmar Schweigert (2007)

Discussiones Mathematicae - General Algebra and Applications

Derived varieties were invented by P. Cohn in [4]. Derived varieties of a given type were invented by the authors in [10]. In the paper we deal with the derived variety $V_{σ}$ of a given variety, by a fixed hypersubstitution σ. We introduce the notion of the dimension of a variety as the cardinality κ of the set of all proper derived varieties of V included in V. We examine dimensions of some varieties in the lattice of all varieties of a given type τ. Dimensions of varieties of lattices and all subvarieties...

The embedding of the formal concept analysis into the L-Fuzzy concept theory.

Ana Burusco Juandeaburre, Ramón Fuentes-González (1998)

Mathware and Soft Computing

In this work, we study the relation between the concept lattice of Wille ([5], [6]) and the L-Fuzzy concept lattice ([2]) developed by us. To do it, we have defined an application g that associates to each concept of Wille an L-Fuzzy concept. The main point of this work is to prove that if we are working with a crisp relation between an object set and an attribute set, the concept lattice of Wille is a sublattice of the L-Fuzzy concept lattice. At the end, we show a typical example in the formal...

The existence of upper semicomplements in lattices of primitive classes

Jaroslav Ježek (1971)

Commentationes Mathematicae Universitatis Carolinae

The facial structure of the finite dimensional latticial cone.

Németh, A.B. (2004)

Mathematica Pannonica

The free compact lattice generated by a topological semilattice.

J.W. Stepp (1975)

Journal für die reine und angewandte Mathematik

The free lattice with 3 generators over $N_{5}$

Waterman, Alan G. (1967)

Portugaliae mathematica

The graphs of join-semilattices and the shape of congruence lattices of particle lattices

Pavel Růžička (2017)

Commentationes Mathematicae Universitatis Carolinae

We attach to each $〈 0, \lor 〉$ -semilattice $S$ a graph $G_{S}$ whose vertices are join-irreducible elements of $S$ and whose edges correspond to the reflexive dependency relation. We study properties of the graph $G_{S}$ both when $S$ is a join-semilattice and when it is a lattice. We call a $〈 0, \lor 〉$ -semilattice $S$ particle provided that the set of its join-irreducible elements satisfies DCC and join-generates $S$ . We prove that the congruence lattice of a particle lattice is anti-isomorphic to the lattice of all hereditary subsets of...