### Localization of semi-Heyting algebras

#### Abstract

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 F−multiplier, where F is a topology on a semi-Heyting algebra L, which is used to construct the localization semi-Heyting algebra LF. Furthermore, we prove that the semi-Heyting algebra of fractions LS associated with an ^−closed system S of L is a semi-Heyting of localization. Finally, in the finite case we prove that LS 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 [11].