E104 - Institut für Diskrete Mathematik und Geometrie
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Journal:
Soft Computing
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ISSN:
1432-7643
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Date (published):
2017
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Number of Pages:
5
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Publisher:
SPRINGER
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Peer reviewed:
Yes
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Keywords:
Convex class; Convex congruence; Algebra with induced order; BCK-algebra; BCI-algebra
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Abstract:
For an algebra A belonging to a quasivariety K, the quotient A/Θ need not belong to K for every Θ∈Con A. The natural question arises for which Θ∈Con A,A/Θ∈K. We consider algebras A=(A,,1) of type (2, 0) where a partial order relation is determined by the operations and 1. Within these, we characterize congruences on A for which A/Θ belongs to the same quasivariety as A. In several particular cases, these congruences are determined by the property that every class is a convex subset of A.
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Additional information:
The final publication is available at Springer via <a href="https://doi.org/10.1007/s00500-016-2306-8" target="_blank">https://doi.org/10.1007/s00500-016-2306-8</a>.
CC BY 4.0
