| 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 |
| . |
| Category:
|
math |
| . |
| 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 |
| . |
| Date available:
|
2009-09-24T21:18:06Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126108 |
| . |
| 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.) |
| . |
