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MATHEMATICA BOHEMICA, Vol. 121, No. 2, pp. 177-182, 1996
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$\Sigma$-hamiltonian and $\Sigma$-regular algebraic structures

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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:**

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