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Are basic algebras residuated structures?

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Abstract

MV-algebras are bounded commutative integral residuated lattices satisfying the double negation and the divisibility laws. Basic algebras were introduced as a certain generalization of MV-algebras (where associativity and commutativity of the binary operation is neglected). Hence, there is a natural question if also basic algebras can be considered as residuated lattices. We prove that for commutative basic algebras it is the case and for non-commutative ones we involve a modified adjointness condition which gives rise a new generalization of a residuated lattice.

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Authors and Affiliations

  1. Department of Algebra and Geometry, Palacký University Olomouc, Tomkova 40, 779 00, Olomouc, Czech Republic

    Michal Botur, Ivan Chajda & Radomír Halaš

Authors
  1. Michal Botur
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  2. Ivan Chajda
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  3. Radomír Halaš
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Corresponding author

Correspondence to Michal Botur.

Additional information

The research was supported by the Research and Development Council of Czech Government via project MSN 6198959214.

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Botur, M., Chajda, I. & Halaš, R. Are basic algebras residuated structures?. Soft Comput 14, 251–255 (2010). https://doi.org/10.1007/s00500-009-0399-z

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