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The Galois correspondence between subvariety lattices and monoids of hpersubstitutions

Klaus Denecke, Jennifer Hyndman, Shelly L. Wismath (2000)

Discussiones Mathematicae - General Algebra and Applications

Denecke and Reichel have described a method of studying the lattice of all varieties of a given type by using monoids of hypersubstitutions. In this paper we develop a Galois correspondence between monoids of hypersubstitutions of a given type and lattices of subvarieties of a given variety of that type. We then apply the results obtained to the lattice of varieties of bands (idempotent semigroups), and study the complete sublattices of this lattice obtained through the Galois correspondence.

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 , ∨ 〉 -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 , ∨ 〉 -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...

The Milgram non-operad

Michael Brinkmeier (1999)

Annales de l'institut Fourier

C. Berger claimed to have constructed an E n -operad-structure on the permutohedras, whose associated monad is exactly the Milgram model for the free loop spaces. In this paper I will show that this statement is not correct.

The niche graphs of interval orders

Jeongmi Park, Yoshio Sano (2014)

Discussiones Mathematicae Graph Theory

The niche graph of a digraph D is the (simple undirected) graph which has the same vertex set as D and has an edge between two distinct vertices x and y if and only if N+D(x) ∩ N+D(y) ≠ ∅ or N−D(x) ∩ N−D(y) ≠ ∅, where N+D(x) (resp. N−D(x)) is the set of out-neighbors (resp. in-neighbors) of x in D. A digraph D = (V,A) is called a semiorder (or a unit interval order ) if there exist a real-valued function f : V → R on the set V and a positive real number δ ∈ R such that (x, y) ∈ A if and only if...

The ordering of commutative terms

Jaroslav Ježek (2006)

Czechoslovak Mathematical Journal

By a commutative term we mean an element of the free commutative groupoid F of infinite rank. For two commutative terms a , b write a ≤ b if b contains a subterm that is a substitution instance of a . With respect to this relation, F is a quasiordered set which becomes an ordered set after the appropriate factorization. We study definability in this ordered set. Among other things, we prove that every commutative term (or its block in the factor) is a definable element. Consequently, the ordered set has...

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