Geodesic
New operations on partial Abelian monoids defined by preideals
Kybernetika, Tome 44 (2008) no. 3, pp. 441-450 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
Classification : 08A55, 81P10
Keywords: partial abelian monoid; generalized effect algebra; preideal; Riesz decomposition property; central element 
@article{KYB_2008_44_3_a12,
     author = {Vincekov\'a, Elena},
     title = {New operations on partial {Abelian} monoids defined by preideals},
     journal = {Kybernetika},
     pages = {441--450},
     year = {2008},
     volume = {44},
     number = {3},
     mrnumber = {2436043},
     zbl = {1154.81305},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2008_44_3_a12/}
}
TY  - JOUR
AU  - Vinceková, Elena
TI  - New operations on partial Abelian monoids defined by preideals
JO  - Kybernetika
PY  - 2008
SP  - 441
EP  - 450
VL  - 44
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/KYB_2008_44_3_a12/
LA  - en
ID  - KYB_2008_44_3_a12
ER  - 
%0 Journal Article
%A Vinceková, Elena
%T New operations on partial Abelian monoids defined by preideals
%J Kybernetika
%D 2008
%P 441-450
%V 44
%N 3
%U http://geodesic.mathdoc.fr/item/KYB_2008_44_3_a12/
%G en
%F KYB_2008_44_3_a12
Vinceková, Elena. New operations on partial Abelian monoids defined by preideals. Kybernetika, Tome 44 (2008) no. 3, pp. 441-450. http://geodesic.mathdoc.fr/item/KYB_2008_44_3_a12/

[1] Dvurečenskij A., Pulmannová S.: New Trends in Quantum Structures. Kluwer Academic Publishers, Dordrecht 2000 | MR

[2] Foulis D. J., Bennett M. K.: Effect algebras and unsharp quantum logics. Found. Phys. 24 (1994), 1325–1346 | MR

[3] Hedlíková J., Pulmannová S.: Generalized difference posets and orthoalgebras. Acta Math. Univ. Comenian. 45 (1996), 247–279 | MR | Zbl

[4] Pulmannová S., Vinceková E.: Riesz ideals in generalized effect algebras and in their unitizations. Algebra Universalis 57 (2007), 4, 393–417 | MR | Zbl

[5] Riečanová Z., Marinová I.: Generalized homogeneous, prelattice and MV-effect algebras. Kybernetika 41 (2005), 2, 129–142 | MR