Results 1 to 10 of about 415 (69)

Structure of Quasivariety Lattices. IV. Nonstandard Quasivarieties

Siberian Mathematical Journal, 2021
Let \(\sigma\) be a finite signature and let \(\mathcal M\) be a quasivariety of signature \(\sigma\). According to Definition 4 of the paper, a class \(\mathcal A=\{\mathbb A_X\;|\;X\in {\mathcal P}_{\textrm{fin}}(\omega)\}\subseteq {\mathcal M}\) of finite \(\sigma\)-structures is called a \textit{finite \(B\)-class} with respect to \(\mathcal M\) if
Kravchenko, A. V., Nurakunov, A. M., Schwidefsky, M. V.   +2 more
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Lattices of quasi-equational theories as congruence lattices of semilattices with operators, Part I [PDF]

, 2012
We show that for every quasivariety K of structures (where both functions and relations are allowed) there is a semilattice S with operators such that the lattice of quasi-equational theories of K (the dual of the lattice of sub-quasivarieties of K) is ...
Adaricheva K. V., Gorbunov V., Gorbunov V., Hofmann R., J. B. NATION, KIRA ADARICHEVA, Schmidt E. T.   +6 more
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Admissibility in Finitely Generated Quasivarieties [PDF]

, 2013
Checking the admissibility of quasiequations in a finitely generated (i.e., generated by a finite set of finite algebras) quasivariety Q amounts to checking validity in a suitable finite free algebra of the quasivariety, and is therefore decidable ...
Metcalfe, George, Röthlisberger, Christoph   +1 more
core   +4 more sources

Some non-standard quasivarieties of lattices

BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS, 2023
The questions of the standardness of quasivarieties have been investigated by many authors. The problem "Which finite lattices generate a standard topological prevariety?" was suggested by D.M. Clark, B.A. Davey, M.G. Jackson and J.G. Pitkethly in 2008. We continue to study the standardness problem for one specific finite modular lattice which does not
S.M. Lutsak, A.O. Basheyeva, A.M. Asanbekov, O.A. Voronina   +3 more
openaire   +3 more sources

Singly generated quasivarieties and residuated structures [PDF]

, 2019
A quasivariety K of algebras has the joint embedding property (JEP) iff it is generated by a single algebra A. It is structurally complete iff the free countably generated algebra in K can serve as A.
Anderson A. R., Bergman C., Chang C. C., Citkin A. I., Citkin A. I., Dywan Z., Esakia L. L., Esakia L. L., Galatos N., Gorbunov V. A., Jónsson B., Kuznetsov A. V., Magari R., Maltsev A. I., Maltsev A. I., Maltsev A. I., Minari P., Pogorzelski W. A., Pogorzelski W. A., Prucnal T., Rybakov V. V., Wroński A., Wroński A., Wroński A., Łoś J., Łoś J.   +25 more
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Admissibility via Natural Dualities [PDF]

, 2015
It is shown that admissible clauses and quasi-identities of quasivarieties generated by a single finite algebra, or equivalently, the quasiequational and universal theories of their free algebras on countably infinitely many generators, may be ...
Cabrer, Leonardo Manuel, Metcalfe, George   +1 more
core   +3 more sources

The possible values of critical points between strongly congruence-proper varieties of algebras [PDF]

, 2014
We denote by Conc(A) the semilattice of all finitely generated congruences of an (universal) algebra A, and we define Conc(V) as the class of all isomorphic copies of all Conc(A), for A in V, for any variety V of algebras.
Elliott, Freese, Gillibert, Gillibert, Gillibert, Gillibert, Goodearl, Gorbunov, Grätzer, Hobby, Huhn, Huhn, Huhn, Kearnes, Pierre Gillibert, Ploščica, Ploščica, Ploščica, Ploščica, Ploščica, Růžička, Růžička, Tůma, Wehrung, Wehrung   +24 more
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Radicals of 0-regular algebras [PDF]

, 2006
We consider a generalisation of the Kurosh--Amitsur radical theory for rings (and more generally multi-operator groups) which applies to 0-regular varieties in which all operations preserve 0.
McConnell, N. R., Stokes, Tim E.
core   +1 more source

Lattices of Quasivarieties of 3-Element Algebras

Journal of Algebra, 1994
This well-written paper contains many interesting results from the structure of lattices of subquasivarieties. A quasivariety is any class of similar algebraic structures that is closed under isomorphisms, substructures, direct products, and ultraproducts.
Adams, M.E., Dziobiak, W.
openaire   +2 more sources

Varieties of distributive rotational lattices [PDF]

, 2013
A rotational lattice is a structure (L;\vee,\wedge, g) where L=(L;\vee,\wedge) is a lattice and g is a lattice automorphism of finite order. We describe the subdirectly irreducible distributive rotational lattices.
A.H. Clifford, B. Jónsson, G. Czédli, G. Czédli, G. Grätzer, G. Grätzer, Gábor Czédli, H. Werner, I. Chajda, I. Chajda, Ivan Chajda, J.D.H. Smith, Radomír Halaš, W. Taylor, W.D. Neumann   +14 more
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