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On order types of linear basic algebras

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Abstract

Basic algebras form a common generalization of MV-algebras and of orthomodular lattices, the algebraic tool for axiomatization of many-valued Łukasiewicz logic and the logic of quantum mechanics. Hence, they are included among the socalled quantum structures. An important role is played by linearly ordered basic algebras because every subdirectly irreducible MV-algebra and every subdirectly irreducible commutative basic algebra is linearly ordered. Since subdirectly irreducible linearly ordered basic algebras exist of any infinite cardinality, the natural question is to describe all possible order types of these algebras. This problem is solved in the paper.

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Authors and Affiliations

  1. Novosibirsk State Technical University, Novosibirsk, Russia

    Alexander G. Pinus

  2. Department of Algebra and Geometry, Palacký University Olomouc, 17. listopadu 12, 771 46, Olomouc, Czech Republic

    Ivan Chajda & Radomír Halaš

Authors
  1. Alexander G. Pinus
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  2. Ivan Chajda
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  3. Radomír Halaš
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Corresponding author

Correspondence to Radomír Halaš.

Additional information

Presented by S. Pulmannova.

The work of the first author is supported by Ministry for Education and Science of the Russian Federation by State Assigment 2014/138 (Grant 1052). The second and the third author is supported by the project Algebraic Methods of Quantum Logic by ESF, CZ.1.07./2.3.00/20.0051.

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Pinus, A.G., Chajda, I. & Halaš, R. On order types of linear basic algebras. Algebra Univers. 73, 267–275 (2015). https://doi.org/10.1007/s00012-015-0328-1

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  • DOI: https://doi.org/10.1007/s00012-015-0328-1

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