Extended Ideals in MV-Algebras

Abstract

In this paper, we introduce the notion of extended of an ideal associated to a subset of an [Formula: see text]-algebra [Formula: see text] and investigate the related properties. A characterization of this extended ideal is given. We show that [Formula: see text] is stable ideal relative to [Formula: see text] such that [Formula: see text] if and only if [Formula: see text] is chain [Formula: see text]-algebra. Finally, the class [Formula: see text] of all stable ideals relative to [Formula: see text] is also a complete Heyting algebra, for an [Formula: see text]-algebra [Formula: see text].