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Title: $\Sigma$-Hamiltonian and $\Sigma$-regular algebraic structures (English)
Author: Chajda, Ivan
Author: Emanovský, Petr
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959 (print)
ISSN: 2464-7136 (online)
Volume: 121
Issue: 2
Year: 1996
Pages: 177-182
Summary lang: English
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Category: math
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Summary: The concept of a $\SS$-closed subset was introduced in [1] for an algebraic structure $\A=(A,F,R)$ of type $\t$ and a set $\SS$ of open formulas of the first order language $L(\t)$. The set $C_\SS(\A)$ of all $\SS$-closed subsets of $\A$ forms a complete lattice whose properties were investigated in [1] and [2]. An algebraic structure $\A$ is called $\SS$- hamiltonian, if every non-empty $\SS$-closed subset of $\A$ is a class (block) of some congruence on $\A$; $\A$ is called $\SS$- regular, if $\0=\F$ for every two $\0$, $\F\in\Con\A$ whenever they have a congruence class $B\in C_\SS(\A)$ in common. This paper contains some results connected with $\SS$-regularity and $\SS$-hamiltonian property of algebraic structures. (English)
Keyword: closure system
Keyword: algebraic structure
Keyword: $\SS$-closed subset
Keyword: $\SS$-hamiltonian and $\SS$-regular algebraic structure
Keyword: $\SS$-transferable congruence
MSC: 03E20
MSC: 04A05
MSC: 08A05
MSC: 08A30
idZBL: Zbl 0863.08001
idMR: MR1400610
DOI: 10.21136/MB.1996.126108
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Date available: 2009-09-24T21:18:06Z
Last updated: 2020-07-29
Stable URL: http://hdl.handle.net/10338.dmlcz/126108
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Reference: [1] Chajda I., Emanovský P.: $\Sigma$-isomorphic algebraic structures.Math. Bohem. 120 (1995), 71-81. Zbl 0833.08001, MR 1336947
Reference: [2] Chajda I., Emanovský P.: Modularity and distributivity of the lattice of $\Sigma$-closed subsets of an algebraic structure.Math. Bohem. 120 (1995), 209-217. MR 1357603
Reference: [3] Chajda I.: Characterization of Hamiltonian algebras.Czechoslovak Math. J. 42(117) (1992), 487-489. MR 1179311
Reference: [4] Chajda I.: Transferable principal congruences and regular algebras.Math. Slovaca 34 (1984), 97-102. Zbl 0601.08004, MR 0735940
Reference: [5] Chajda I.: Algebras whose principal congruences form a sublattices of the congruence lattice.Czechoslovak Math. J. 38 (113) (1988), 585-588. MR 0962902
Reference: [6] Grätzer G.: Universal Algebra.(2nd edition). Springer Verlag, 1979. MR 0538623
Reference: [7] Kiss E. W.: Each Hamiltonian variety has the congruence extension property.Algebra Universalis 12 (1981), 395-398. Zbl 0422.08003, MR 0624304, 10.1007/BF02483899
Reference: [8] Klukovits L.: Hamiltonian varieties of universal algebras.Acta Sci. Math. (Szeged) 37 (1975), 11-15. Zbl 0285.08004, MR 0401611
Reference: [9] Malcev A.I.: Algebraic Systems.Nauka, Moskva, 1970. (In Russian.) MR 0282908
Reference: [10] Mamedov O.M.: Characterization of varieties with n-transferable principal congruences.VINITI Akad. Nauk Azerbaid. SR, Inst. Matem. i Mech. (Baku), 1989, pp. 2-12. (In Russian.)
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