New operations on partial Abelian monoids defined by preideals

Elena Vinceková

Kybernetika (2008)

  • Volume: 44, Issue: 3, page 441-450
  • ISSN: 0023-5954

Abstract

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We consider partial abelian monoids, in particular generalized effect algebras. From the given structures, we construct new ones by introducing a new operation ⊕ , which is given by restriction of the original partial operation + with respect to a special subset called preideal. We bring some derived properties and characterizations of these new built structures, supporting the results by illustrative examples.

How to cite

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Vinceková, Elena. "New operations on partial Abelian monoids defined by preideals." Kybernetika 44.3 (2008): 441-450. <http://eudml.org/doc/33939>.

@article{Vinceková2008,
abstract = {We consider partial abelian monoids, in particular generalized effect algebras. From the given structures, we construct new ones by introducing a new operation $\oplus $, which is given by restriction of the original partial operation + with respect to a special subset called preideal. We bring some derived properties and characterizations of these new built structures, supporting the results by illustrative examples.},
author = {Vinceková, Elena},
journal = {Kybernetika},
keywords = {partial abelian monoid; generalized effect algebra; preideal; Riesz decomposition property; central element; partial abelian monoid; generalized effect algebra; preideal; Riesz decomposition property; central element},
language = {eng},
number = {3},
pages = {441-450},
publisher = {Institute of Information Theory and Automation AS CR},
title = {New operations on partial Abelian monoids defined by preideals},
url = {http://eudml.org/doc/33939},
volume = {44},
year = {2008},
}

TY - JOUR
AU - Vinceková, Elena
TI - New operations on partial Abelian monoids defined by preideals
JO - Kybernetika
PY - 2008
PB - Institute of Information Theory and Automation AS CR
VL - 44
IS - 3
SP - 441
EP - 450
AB - We consider partial abelian monoids, in particular generalized effect algebras. From the given structures, we construct new ones by introducing a new operation $\oplus $, which is given by restriction of the original partial operation + with respect to a special subset called preideal. We bring some derived properties and characterizations of these new built structures, supporting the results by illustrative examples.
LA - eng
KW - partial abelian monoid; generalized effect algebra; preideal; Riesz decomposition property; central element; partial abelian monoid; generalized effect algebra; preideal; Riesz decomposition property; central element
UR - http://eudml.org/doc/33939
ER -

References

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  1. Dvurečenskij A., Pulmannová S., New Trends in Quantum Structures, Kluwer Academic Publishers, Dordrecht 2000 MR1861369
  2. Foulis D. J., Bennett M. K., Effect algebras and unsharp quantum logics, Found. Phys. 24 (1994), 1325–1346 (1994) MR1304942
  3. Hedlíková J., Pulmannová S., Generalized difference posets and orthoalgebras, Acta Math. Univ. Comenian. 45 (1996), 247–279 (1996) Zbl0922.06002MR1451174
  4. Pulmannová S., Vinceková E., Riesz ideals in generalized effect algebras and in their unitizations, Algebra Universalis 57 (2007), 4, 393–417 Zbl1139.81007MR2373250
  5. Riečanová Z., Marinová I., Generalized homogeneous, prelattice and MV-effect algebras, Kybernetika 41 (2005), 2, 129–142 MR2138764

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