MATHEMATICA BOHEMICA, Vol. 121, No. 2, pp. 177-182, 1996

$\Sigma$-hamiltonian and $\Sigma$-regular algebraic structures

Ivan Chajda, Petr Emanovsky

Ivan Chajda, katedra algebry a geometrie, Prir. fak. UP Olomouc, Tomkova 40, 779 00 Olomouc; Petr Emanovsky, katedra matematiky, Ped. fak. UP Olomouc, Zizkovo nam. 5, 771 40 Olomouc, Czech Republic

Abstract: The concept of a $\Sigma$-closed subset was introduced earlier by the authors for an algebraic structure $\Cal A=(A,F,R)$ of type $\tau$ and a set $\Sigma$ of open formulas of the first order language $L(\tau)$. The set $C_\Sigma(\Cal A)$ of all $\Sigma$-closed subsets of $\Cal A$ forms a complete lattice whose properties were investigated in two previous papers by the authors. An algebraic structure $\Cal A$ is called $\Sigma$- hamiltonian, if every non-empty $\Sigma$-closed subset of $\Cal A$ is a class (block) of some congruence on $\Cal A$;$\Cal A$ is called $\Sigma$- regular, if $\theta=\Phi$ for every two $\theta$, $\Phi\in\operatorname{Con}\Cal A$ whenever they have a congruence class $B\in C_\Sigma(\Cal A)$ in common. This paper contains some results connected with $\Sigma$-regularity and $\Sigma$-hamiltonian property of algebraic structures.

Keywords: algebraic structure, closure system, $\Sigma$-closed subset, $\Sigma$-hamiltonian and $\Sigma$-regular algebraic structure, $\Sigma$-transferable congruence

Classification (MSC91): 08A05, 04A05

Full text of the article:

[Previous Article] [Next Article] [Contents of this Number] [Journals Homepage]