Congruences and ideals in lattice effect algebras as basic algebras

Sylvia Pulmannová; Elena Vinceková

Kybernetika (2009)

  • Volume: 45, Issue: 6, page 1030-1039
  • ISSN: 0023-5954

Abstract

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Effect basic algebras (which correspond to lattice ordered effect algebras) are studied. Their ideals are characterized (in the language of basic algebras) and one-to-one correspondence between ideals and congruences is shown. Conditions under which the quotients are OMLs or MV-algebras are found.

How to cite

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Pulmannová, Sylvia, and Vinceková, Elena. "Congruences and ideals in lattice effect algebras as basic algebras." Kybernetika 45.6 (2009): 1030-1039. <http://eudml.org/doc/37679>.

@article{Pulmannová2009,
abstract = {Effect basic algebras (which correspond to lattice ordered effect algebras) are studied. Their ideals are characterized (in the language of basic algebras) and one-to-one correspondence between ideals and congruences is shown. Conditions under which the quotients are OMLs or MV-algebras are found.},
author = {Pulmannová, Sylvia, Vinceková, Elena},
journal = {Kybernetika},
keywords = {basic algebra; effect algebra; ideal; congruence; dependence ordering; FGM distribution; measures of association; symmetry},
language = {eng},
number = {6},
pages = {1030-1039},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Congruences and ideals in lattice effect algebras as basic algebras},
url = {http://eudml.org/doc/37679},
volume = {45},
year = {2009},
}

TY - JOUR
AU - Pulmannová, Sylvia
AU - Vinceková, Elena
TI - Congruences and ideals in lattice effect algebras as basic algebras
JO - Kybernetika
PY - 2009
PB - Institute of Information Theory and Automation AS CR
VL - 45
IS - 6
SP - 1030
EP - 1039
AB - Effect basic algebras (which correspond to lattice ordered effect algebras) are studied. Their ideals are characterized (in the language of basic algebras) and one-to-one correspondence between ideals and congruences is shown. Conditions under which the quotients are OMLs or MV-algebras are found.
LA - eng
KW - basic algebra; effect algebra; ideal; congruence; dependence ordering; FGM distribution; measures of association; symmetry
UR - http://eudml.org/doc/37679
ER -

References

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  1. Congruences and ideals of effect algebras, Order 20 (2003), 67–77. MR1993411
  2. Many valued quantum algebras, Alg. Univ. 60 (2009), 63–90. MR2480632
  3. Algebraic analysis of many valued logics, Trans. Amer. Math. Soc. 88 (1958), 467–490. Zbl0084.00704MR0094302
  4. Boolean D-posets, Tatra Mt. Math. Publ. 10 (1997), 1–15. MR1469294
  5. New Trends in Quantum Structures, Kluwer Academic Publishers, Dordrecht 2000. MR1861369
  6. Effect algebras and unsharp quantum logics, Found. Phys. 24 (1994), 1331–1352. MR1304942
  7. Quantum MV-algebras, Studia Logica 56 (1996), 303–417. Zbl1093.06011MR1397488
  8. Total extensions of effect algebras, Found. Phys. Lett. 8 (1995), 243–252. MR1339403
  9. Ideals and quotients in lattice ordered effect albebras, Soft Computing 5 (2001), 376–380. 
  10. D-posets, Math. Slovaca 44 (1994), 21–34. MR1290269

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