Horizontal sums of basic algebras

Ivan Chajda

Discussiones Mathematicae - General Algebra and Applications (2009)

  • Volume: 29, Issue: 1, page 21-33
  • ISSN: 1509-9415

Abstract

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The variety of basic algebras is closed under formation of horizontal sums. We characterize when a given basic algebra is a horizontal sum of chains, MV-algebras or Boolean algebras.

How to cite

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Ivan Chajda. "Horizontal sums of basic algebras." Discussiones Mathematicae - General Algebra and Applications 29.1 (2009): 21-33. <http://eudml.org/doc/276930>.

@article{IvanChajda2009,
abstract = {The variety of basic algebras is closed under formation of horizontal sums. We characterize when a given basic algebra is a horizontal sum of chains, MV-algebras or Boolean algebras.},
author = {Ivan Chajda},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {Basic algebra; horizontal sum; chain basic algebra; MV-algebra; Boolean algebra},
language = {eng},
number = {1},
pages = {21-33},
title = {Horizontal sums of basic algebras},
url = {http://eudml.org/doc/276930},
volume = {29},
year = {2009},
}

TY - JOUR
AU - Ivan Chajda
TI - Horizontal sums of basic algebras
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2009
VL - 29
IS - 1
SP - 21
EP - 33
AB - The variety of basic algebras is closed under formation of horizontal sums. We characterize when a given basic algebra is a horizontal sum of chains, MV-algebras or Boolean algebras.
LA - eng
KW - Basic algebra; horizontal sum; chain basic algebra; MV-algebra; Boolean algebra
UR - http://eudml.org/doc/276930
ER -

References

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  1. [1] I. Chajda, Lattices and semilattices having an antitone involution in every upper interval, Comment. Math. Univ. Carolinae 44 (2003), 577-585. Zbl1101.06003
  2. [2] I. Chajda, R. Halaš and J. Kühr, Semilattice Structures, Heldermann Verlag, Lemgo (Germany), 2007, 228pp, ISBN 978-3-88538-230-0. 
  3. [3] I. Chajda, R. Halaš and J. Kühr, Many-valued quantum algebras, Algebra Universalis 60 (2009), 63-90. %DOI 10.1007/s00012-008-2086-9. Zbl1219.06013
  4. [4] I. Chajda and H. Länger, A characterization of horizontal sums of Boolean rings, Contributions to General Algebra 18, Proceedings of the conference Arbeitstagung Allgemeine Algebra 73, Klagenfurt 2007, Verlag J. Heyn, Klagenfurt (2007), 23-30. Zbl1148.06009
  5. [5] A. Dvurečenskij and S. Pulmannová, New Trends in Quantum Structures, Kluwer Acad. Publ., Dordrecht 2000. Zbl0987.81005
  6. [6] D.J. Foulis and M.K. Bennett, Effect algebras and unsharp quantum logic, Found. Phys. 24 (1994), 1325-1346. 
  7. [7] Z. Riečanová, Generalization of blocks for D-lattices and lattice-ordered effect algebras, Intern. J. Theor. Phys. 39 (2000), 231-237. Zbl0968.81003
  8. [8] N. Vaserstein, Non-commutative number theory, Contemp. Math. 83 (1989), 445-449 

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