# Horizontal sums of basic algebras

Discussiones Mathematicae - General Algebra and Applications (2009)

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

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topIvan 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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- [2] I. Chajda, R. Halaš and J. Kühr, Semilattice Structures, Heldermann Verlag, Lemgo (Germany), 2007, 228pp, ISBN 978-3-88538-230-0.
- [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] 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] A. Dvurečenskij and S. Pulmannová, New Trends in Quantum Structures, Kluwer Acad. Publ., Dordrecht 2000. Zbl0987.81005
- [6] D.J. Foulis and M.K. Bennett, Effect algebras and unsharp quantum logic, Found. Phys. 24 (1994), 1325-1346.
- [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] N. Vaserstein, Non-commutative number theory, Contemp. Math. 83 (1989), 445-449

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