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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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