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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
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
Citation:
V. L. Usol'tsev, “On Hamiltonian ternary algebras with operators”, Chebyshevskii Sb., 15:3 (2014), 100–113
Linking options:
https://www.mathnet.ru/eng/cheb354 https://www.mathnet.ru/eng/cheb/v15/i3/p100
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Abstract page: | 245 | Full-text PDF : | 73 | References: | 55 |
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