Figallo, Aldo V.; Pelaitay, Gustavo Localization of semi-Heyting algebras. (English) Zbl 1413.06013 An. Univ. Craiova, Ser. Mat. Inf. 43, No. 2, 210-217 (2016). 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) Keywords:localization; \(\mathcal F\)-multipliers, semi-Heyting algebras; \(\wedge\)-closed system Citations:Zbl 1053.03520 PDFBibTeX XMLCite \textit{A. V. Figallo} and \textit{G. Pelaitay}, An. Univ. Craiova, Ser. Mat. Inf. 43, No. 2, 210--217 (2016; Zbl 1413.06013)