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Modyfications of Csákány's Theorem

Ivan Chajda (2000)

Discussiones Mathematicae - General Algebra and Applications

Varieties whose algebras have no idempotent element were characterized by B. Csákány by the property that no proper subalgebra of an algebra of such a variety is a congruence class. We simplify this result for permutable varieties and we give a local version of the theorem for varieties with nullary operations.

Monotone interval eigenproblem in max–min algebra

Martin Gavalec, Ján Plavka (2010)

Kybernetika

The interval eigenproblem in max-min algebra is studied. A classification of interval eigenvectors is introduced and six types of interval eigenvectors are described. Characterization of all six types is given for the case of strictly increasing eigenvectors and Hasse diagram of relations between the types is presented.

Monounary algebras with two direct limits

Emília Halušková (2000)

Mathematica Bohemica

In this paper we describe all algebras A with one unary operation such that by a direct limit construction exactly two nonisomorphic algebras can be obtained from A .

Morphisms fixing words associated with exchange of three intervals

Petr Ambrož, Zuzana Masáková, Edita Pelantová (2010)

RAIRO - Theoretical Informatics and Applications

We consider words coding exchange of three intervals with permutation (3,2,1), here called 3iet words. Recently, a characterization of substitution invariant 3iet words was provided. We study the opposite question: what are the morphisms fixing a 3iet word? We reveal a narrow connection of such morphisms and morphisms fixing Sturmian words using the new notion of amicability.

Morphisms preserving the set of words coding three interval exchange

Tomáš Hejda (2012)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Any amicable pair ϕ, ψ of Sturmian morphisms enables a construction of a ternary morphism η which preserves the set of infinite words coding 3-interval exchange. We determine the number of amicable pairs with the same incidence matrix in SL±(2,ℕ) and we study incidence matrices associated with the corresponding ternary morphisms η.

Morphisms preserving the set of words coding three interval exchange∗∗∗

Tomáš Hejda (2012)

RAIRO - Theoretical Informatics and Applications

Any amicable pair ϕ, ψ of Sturmian morphisms enables a construction of a ternary morphism η which preserves the set of infinite words coding 3-interval exchange. We determine the number of amicable pairs with the same incidence matrix in SL±(2,ℕ) and we study incidence matrices associated with the corresponding ternary morphisms η.

M-Solid Subvarieties of some Varieties of Commutative Semigroups

Koppitz, J. (1997)

Serdica Mathematical Journal

∗ The research of the author was supported by the Alexander v. Humboldt-Stiftung.The basic concepts are M -hyperidentities, where M is a monoid of hypersubstitutions. The set of all M -solid varieties of semigroups forms a complete sublattice of the lattice of all varieties of semigroups. We fix some specific varieties V of commutative semigroups and study the set of all M -solid subvarieties of V , in particular, if V is nilpotent.

Multiple left distributive systems

Patrick Dehornoy (1997)

Commentationes Mathematicae Universitatis Carolinae

We describe the free objects in the variety of algebras involving several mutually distributive binary operations. Also, we show how an associative operation can be constructed on such systems in good cases, thus obtaining a two way correspondence between LD-monoids (sets with a left self-distributive and a compatible associative operation) and multi-LD-systems (sets with a family of mutually distributive operations).

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