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Pre-ideals of Basic Algebras

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Abstract

Basic algebras are a generalization of MV-algebras, also including orthomodular lattices and lattice effect algebras. A pre-ideal of a basic algebra is a non-empty subset that is closed under the addition ⊕ and downwards closed with respect to the underlying order. In this paper, we study the pre-ideal lattices of algebras in a particular subclass of basic algebras which are closer to MV-algebras than basic algebras in general. We also prove that finite members of this subclass are exactly finite MV-algebras.

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Authors and Affiliations

  1. Department of Algebra and Geometry, Faculty of Science, Palacký University at Olomouc, 17. listopadu 12, 77146, Olomouc, Czech Republic

    Jan Krňávek & Jan Kühr

Authors
  1. Jan Krňávek
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  2. Jan Kühr
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Correspondence to Jan Kühr.

Additional information

Supported by the Czech Government Research Project MSM6198959214, by the ESF Project CZ.1.07/2.3.00/20.0051, and by the Palacký University Grants PrF2010008 and PrF2011022.

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Krňávek, J., Kühr, J. Pre-ideals of Basic Algebras. Int J Theor Phys 50, 3828–3843 (2011). https://doi.org/10.1007/s10773-011-0928-2

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  • DOI: https://doi.org/10.1007/s10773-011-0928-2

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