For an algebra [Formula: see text] belonging to a quasivariety [Formula: see text], the quotient [Formula: see text] need not belong to [Formula: see text] for every [Formula: see text]. The natural question arises for which [Formula: see text]. We consider algebras [Formula: see text] of type (2, 0) where a partial order relation is determined by the operations [Formula: see text] and 1. Within these, we characterize congruences on [Formula: see text] for which [Formula: see text] belongs to the same quasivariety as [Formula: see text]. In several particular cases, these congruences are determined by the property that every class is a convex subset of A.

Faculty of Mathematics and Geoinformation Institute of Discrete Mathematics and Geometry TU Wien Wiedner Hauptstraße 8 10 1040 Vienna Austria

Faculty of Science Department of Algebra and Geometry Palacký University Olomouc 17 listopadu 12 771 46 Olomouc Czech Republic

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