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Localization of semi-Heyting algebras. (English) Zbl 1413.06013

Summary: In this note, we introduce the notion of ideal on semi-Heyting algebras which allows us to consider a topology on them. Besides, we define the concept of \(\mathcal F\)-multiplier, where \(\mathcal F\) is a topology on a semi-Heyting algebra \(L\), which is used to construct the localization semi-Heyting algebra \(L_\mathcal F\). Furthermore, we prove that the semi-Heyting algebra of fractions \(L_S\) associated with an \(\wedge\)-closed system \(S\) of \(L\) is a semi-Heyting of localization. Finally, in the finite case we prove that \(L_S\) is isomorphic to a special subalgebra of \(L\). Since Heyting algebras are a particular case of semi-Heyting algebras, all these results generalize those obtained in C. Dan [An. Univ. Craiova, Ser. Mat. Inf. 24, 98–109 (1997; Zbl 1053.03520)].

MSC:

06D20 Heyting algebras (lattice-theoretic aspects)

Citations:

Zbl 1053.03520
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