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Chebyshevskii Sbornik, 2014, Volume 15, Issue 3, Pages 100–113 (Mi cheb354)  

This article is cited in 6 scientific papers (total in 6 papers)

On Hamiltonian ternary algebras with operators

V. L. Usol'tsev

Volgograd State Social and Pedagogical University, Russia, 400131, Volgograd, Lenina av., 27
Full-text PDF (588 kB) Citations (6)
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Abstract: In this work is given the description of Hamiltonian algebras in some subclasses of class of algebras with operators having one ternary basic operation and one operator. Universal algebra A is a Hamiltonian algebra if every subuniverse of A is the block of some congruence of the algebra A. Algebra with operators is an universal algebra with additional system of the unary operations acting as endomorphisms with respect to basic operations. These operations are called permutable with basic operations. An algebra with operators is ternary if it has exactly one basic operation and this operation is ternary.
It is obtained the sufficient condition of Hamiltonity for arbitrary universal algebras with operators. It is described Hamiltonian algebras in classes of ternary algebras with one operator and with basic operation that is either Pixley operation, or minority function, or majority function of special view.
Let $V$ be a variety of algebras with operators and $V$ has signature $\Omega_1 \cup \Omega_2$, where $\Omega_1$ is an arbitrary signature containing near-unanimity function and $\Omega_2$ is a set of operators. It is proved that $V$ not contains nontrivial Abelian algebras.
Keywords: Hamiltonian algebra, Abelian algebra, algebra with operators, ternary operation, near-unanimity function.
Received: 12.06.2014
Document Type: Article
UDC: 512.579
Language: Russian
Citation: V. L. Usol'tsev, “On Hamiltonian ternary algebras with operators”, Chebyshevskii Sb., 15:3 (2014), 100–113
Citation in format AMSBIB
\Bibitem{Uso14}
\by V.~L.~Usol'tsev
\paper On Hamiltonian ternary algebras with operators
\jour Chebyshevskii Sb.
\yr 2014
\vol 15
\issue 3
\pages 100--113
\mathnet{http://mi.mathnet.ru/cheb354}
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  • https://www.mathnet.ru/eng/cheb/v15/i3/p100
  • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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