Projectability and weak homogeneity of pseudo effect algebras

Ján Jakubík

Czechoslovak Mathematical Journal (2009)

  • Volume: 59, Issue: 1, page 183-196
  • ISSN: 0011-4642

Abstract

top
In this paper we deal with a pseudo effect algebra 𝒜 possessing a certain interpolation property. According to a result of Dvurečenskij and Vettterlein, 𝒜 can be represented as an interval of a unital partially ordered group G . We prove that 𝒜 is projectable (strongly projectable) if and only if G is projectable (strongly projectable). An analogous result concerning weak homogeneity of 𝒜 and of G is shown to be valid.

How to cite

top

Jakubík, Ján. "Projectability and weak homogeneity of pseudo effect algebras." Czechoslovak Mathematical Journal 59.1 (2009): 183-196. <http://eudml.org/doc/37916>.

@article{Jakubík2009,
abstract = {In this paper we deal with a pseudo effect algebra $\mathcal \{A\}$ possessing a certain interpolation property. According to a result of Dvurečenskij and Vettterlein, $\mathcal \{A\}$ can be represented as an interval of a unital partially ordered group $G$. We prove that $\mathcal \{A\}$ is projectable (strongly projectable) if and only if $G$ is projectable (strongly projectable). An analogous result concerning weak homogeneity of $\mathcal \{A\}$ and of $G$ is shown to be valid.},
author = {Jakubík, Ján},
journal = {Czechoslovak Mathematical Journal},
keywords = {pseudo effect algebra; unital partially ordered group; internal direct factor; polar; projectability; strong projectability; weak homogeneity; pseudo effect algebra; unital partially ordered group; internal direct factor; polar; projectability; strong projectability; weak homogeneity},
language = {eng},
number = {1},
pages = {183-196},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Projectability and weak homogeneity of pseudo effect algebras},
url = {http://eudml.org/doc/37916},
volume = {59},
year = {2009},
}

TY - JOUR
AU - Jakubík, Ján
TI - Projectability and weak homogeneity of pseudo effect algebras
JO - Czechoslovak Mathematical Journal
PY - 2009
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 59
IS - 1
SP - 183
EP - 196
AB - In this paper we deal with a pseudo effect algebra $\mathcal {A}$ possessing a certain interpolation property. According to a result of Dvurečenskij and Vettterlein, $\mathcal {A}$ can be represented as an interval of a unital partially ordered group $G$. We prove that $\mathcal {A}$ is projectable (strongly projectable) if and only if $G$ is projectable (strongly projectable). An analogous result concerning weak homogeneity of $\mathcal {A}$ and of $G$ is shown to be valid.
LA - eng
KW - pseudo effect algebra; unital partially ordered group; internal direct factor; polar; projectability; strong projectability; weak homogeneity; pseudo effect algebra; unital partially ordered group; internal direct factor; polar; projectability; strong projectability; weak homogeneity
UR - http://eudml.org/doc/37916
ER -

References

top
  1. Cignoli, R., D'Ottaviano, M. I., Mundici, D., 10.1007/978-94-015-9480-6, Kluwer Dordrecht (2000). (2000) DOI10.1007/978-94-015-9480-6
  2. Darnel, M. R., Theory of Lattice-Ordered Groups, Marcel Dekker New York (1995). (1995) Zbl0810.06016MR1304052
  3. Dvurečenskij, A., Vetterlein, T., 10.1023/A:1004192715509, Inter. J. Theor. Phys. 40 (2001), 685-701. (2001) MR1831592DOI10.1023/A:1004192715509
  4. Dvurečenskij, A., Vetterlein, T., 10.1023/A:1004144832348, Int. J. Theor. Phys. 40 (2001), 703-726. (2001) MR1831593DOI10.1023/A:1004144832348
  5. Dvurečenskij, A., Vetterlein, T., 10.1017/S1446788700008120, J. Aust. Math. Soc. 75 (2003), 295-311. (2003) MR2015319DOI10.1017/S1446788700008120
  6. Georgescu, G., Iorgulescu, A., Pseudo M V -algebras: a noncommutative extension of M V -algebras, In: Proceedings of the Fourth International Symposium on Economic Informatics, Bucharest, 6-9 May, Romania (1999), 961-968. (1999) Zbl0985.06007MR1730100
  7. Georgescu, G., Iorgulescu, A., Pseudo M V -algebras, Mult.-Valued Log. 6 (2001), 95-135. (2001) Zbl1014.06008MR1817439
  8. Jakubík, J., 10.1007/s10587-006-0090-9, Czechoslovak Math. J. 56 (2006), 1215-1227. (2006) Zbl1164.06315MR2280805DOI10.1007/s10587-006-0090-9
  9. Jakubík, J., Weak homogeneity of lattice ordered groups, Czechoslovak Math. J (to appear). MR2356285
  10. Jakubík, J., Direct product decompositions of pseudo effect algebras, Math. Slovaca 55 (2005), 379-398. (2005) MR2181779
  11. Rachůnek, J., 10.1023/A:1021766309509, Czechoslovak Math. J. 52 (2002), 255-273. (2002) MR1905434DOI10.1023/A:1021766309509
  12. Sikorski, R., Boolean Algebras, 2nd edition, Springer Berlin (1964). (1964) MR0177920

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.