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Convex congruences.

Ivan Chajda1, Helmut Länger2

  • 1Faculty of Science, Department of Algebra and Geometry, Palacký University Olomouc, 17. listopadu 12, 771 46 Olomouc, Czech Republic.

Soft Computing
|October 14, 2017
PubMed
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Investigating quasivarieties of algebras, this study identifies specific congruences on algebras of type (2,0) where quotient algebras remain within the same quasivariety. These congruences are linked to convex classes.

Area of Science:

  • Universal algebra
  • Algebraic structures
  • Quasivarieties

Background:

  • Algebras within a quasivariety may not always yield quotient algebras belonging to the same quasivariety.
  • Understanding conditions for quotient algebras to remain within a quasivariety is a key algebraic problem.

Purpose of the Study:

  • To characterize congruences on algebras of type (2,0) that ensure quotient algebras belong to the same quasivariety.
  • To explore the relationship between these congruences and the convexity of algebra classes.

Main Methods:

  • Consideration of algebras of type (2,0) with a partial order defined by operations.
  • Characterization of specific congruences on these algebras.
  • Analysis of the properties of quotient algebras.
Keywords:
Algebra with induced orderBCI-algebraBCK-algebraConvex classConvex congruence

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Main Results:

  • Identified conditions on congruences for quotient algebras to stay within the parent quasivariety.
  • Demonstrated that in specific cases, these congruences correspond to classes being convex subsets.

Conclusions:

  • Provides a characterization of congruences preserving quasivariety membership under quotient operations.
  • Highlights the role of convex subsets in defining such congruences for specific algebra types.