Chajda Ivan, Länger Helmut
Faculty of Science, Department of Algebra and Geometry, Palacký University Olomouc, 17. listopadu 12, 771 46 Olomouc, Czech Republic.
Faculty of Mathematics and Geoinformation, Institute of Discrete Mathematics and Geometry, TU Wien, Wiedner Hauptstraße 8-10, 1040 Vienna, Austria.
Soft comput. 2017;21(19):5641-5645. doi: 10.1007/s00500-016-2306-8. Epub 2016 Aug 9.
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 .
对于属于拟簇(\mathcal{Q})的代数(\mathbf{A})，对于每个(\theta\in\mathrm{Con}(\mathbf{A}))，商(\mathbf{A}/\theta)不一定属于(\mathcal{Q})。于是自然会问对于哪些(\theta)会出现这种情况。我们考虑类型为((2,0))的代数(\mathbf{A})，其中偏序关系由运算(\wedge)和(1)确定。在这些代数中，我们刻画了(\mathbf{A})上的同余关系(\theta)，使得(\mathbf{A}/\theta)与(\mathbf{A})属于同一个拟簇。在几个特殊情况下，这些同余关系由每个类都是(\mathbf{A})的凸子集这一性质确定。
