On order types of linear basic algebras

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• 作者：Alexander G. Pinus ; Ivan Chajda ; Radomír Hala?
• 关键词：Primary ; 06A05 ; Secondary ; 03G25 ; 03D35 ; basic algebra ; commutative basic algebra ; subdirect irreducibility ; linear order ; order type
• 刊名：Algebra Universalis
• 出版年：2015
• 出版时间：June 2015
• 年：2015
• 卷：73
• 期：3-4
• 页码：267-275
• 全文大小：497 KB
• 参考文献：1.Botur, M.: Subdirectly irreducible commutative basic algebras are linearly ordered. PhD thesis, Palacky University Olomouc (2009)
  2.Botur M.: An example of a commutative basic algebra which is not an MV-algebra. Math. Slovaca 60, 171-78 (2010)MATH MathSciNet
  3.Botur, M., Chajda, I.: There exist subdirectly irreducible commutative basic algebras of an arbitrary infinite cardinality which are not MV-algebras. Algebra Universalis 65, 185-92 (2011)
  4.Botur, M., Hala?, R.: Complete commutative basic algebras. Order 24, 89-05 (2007)
  5.Botur, M., Hala?, R.: Finite commutative basic algebras are MV-effect algebras. J. Mult.-Valued Logic Soft Comput. 14, 69-0 (2008).
  6.Botur, M., Kühr, J.: On (finite) distributive lattices with antitone involutions. Soft Computing 18, 1033-040 (2014)
  7.Chajda, I.: Basic algebras and their applications, an overview. Contributions to General Algebra 20, Johannes Heyn, Klagenfurt (2011)
  8.Chajda, I., Hala?, R., Kühr, J.: Semilattice Structures. Heldermann, Lemgo (2007)
  9.Chajda, I., Hala?, R., Kühr, J.: Many-valued quantum algebras. Algebra Universalis 60, 63-0 (2009)
  10.Chajda, I., Kola?ík, M.: Independence of axiom system of basic algebras. Soft Computing 13, 41-3 (2009)
  11.Chajda, I., Kühr, J.: Ideals and congruences of basic algebras. Soft Computing 17, 401-10 (2013)
  12.Comfort, W.W., Negrepontis, S.: The theory of ultrafilters. Die Grundlehren der mathematischen Wissenschaften, vol. 211, Springer, New York (1974)
  13.Gaitán H.: Subdirectly irreducible MV-algebras. Czechoslovak Math. J. 53, 631-39 (2003)View Article MATH MathSciNet
  14.Keisler, H. J.: Model theory for infinitary logic. North-Holland, Amsterdam (1971)
  
• 作者单位：Alexander G. Pinus (1)
  Ivan Chajda (2)
  Radomír Hala? (2)
  
  1. Novosibirsk State Technical University, Novosibirsk, Russia
  2. Department of Algebra and Geometry, Palacky University Olomouc, 17. listopadu 12, 771 46, Olomouc, Czech Republic
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Algebra
  
• 出版者：Birkh盲user Basel
• ISSN：1420-8911

文摘

Basic algebras form a common generalization of MV-algebras and of orthomodular lattices, the algebraic tool for axiomatization of many-valued ?ukasiewicz 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.