| Title:
|
Divisible effect algebras and interval effect algebras (English) |
| Author:
|
Pulmannová, Sylvia |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
42 |
| Issue:
|
2 |
| Year:
|
2001 |
| Pages:
|
219-236 |
| . |
| Category:
|
math |
| . |
| Summary:
|
It is shown that divisible effect algebras are in one-to-one correspondence with unit intervals in partially ordered rational vector spaces. (English) |
| Keyword:
|
effect algebras |
| Keyword:
|
divisible effect algebras |
| Keyword:
|
words |
| Keyword:
|
po-groups |
| MSC:
|
03G12 |
| MSC:
|
06F15 |
| MSC:
|
46N50 |
| MSC:
|
81P10 |
| idZBL:
|
Zbl 1052.03040 |
| idMR:
|
MR1832142 |
| . |
| Date available:
|
2009-01-08T19:09:26Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119238 |
| . |
| Reference:
|
[1] Baer R.: Free sums of groups and their generalizations. An analysis of the associative law.Amer. J. Math. 41 (1949), 706-742. Zbl 0033.34504, MR 0030953 |
| Reference:
|
[2] Bennett M.K., Foulis D.J.: Interval and scale effect algebras.Adv. in Appl. Math. 19 (1997), 200-215. Zbl 0883.03048, MR 1459498 |
| Reference:
|
[3] Bigard A., Keimel K., Wolfenstein S.: Groupes et Anneaux Réticulés.Springer-Verlag, Berlin-Heidelberg-New York, 1977. Zbl 0384.06022, MR 0552653 |
| Reference:
|
[4] Bugajski S.: Fundamentals of fuzzy probability theory.Internat. J. Theoret. Phys. 35 (1996), 2229-2244. Zbl 0872.60003, MR 1423402 |
| Reference:
|
[5] Bush P., Grabowski M., Lahti P.: Operational Quantum Physics.Springer-Verlag, Berlin, 1995. MR 1356220 |
| Reference:
|
[6] Cignoli R., D'Ottaviano I.M.L., Mundici D.: Algebraic Foundations of Many-valued Reasoning.Kluwer Academic Publ., Dordrecht 2000. Zbl 0937.06009, MR 1786097 |
| Reference:
|
[7] Dalla Chiara M.L., Giuntini R.: Quantum logic.in Handbook of Philosophical logic, Eds. D. Gabbay, F. Guenthner, Kluwer Acad. Publ., Dordrecht, to appear. Zbl 0969.03070, MR 1818789 |
| Reference:
|
[8] Dvurečenskij A., Pulmannová S.: New Trends in Quantum Structures.Kluwer Acad. Publ., Dordrecht, 2000. MR 1861369 |
| Reference:
|
[9] Dvurečenskij A., Riečan B.: Weakly divisible MV-algebras and product.J. Math. Anal. Appl. 234 (1999), 208-222. MR 1694841 |
| Reference:
|
[10] Foulis D.J., Bennett M.K.: Effect algebras and unsharp quantum logics.Found. Phys. 37 (1994), 1325-1346. MR 1304942 |
| Reference:
|
[11] Foulis D.J., Greechie R.J., Bennett M.K.: Sums and products of interval effect algebras.Internat. J. Theoret. Phys. 33 (1994), 2119-2136. MR 1311152 |
| Reference:
|
[12] Fuchs L.: Partially Ordered Algebraic Systems.Pergamon Press, Oxford-London-New York-Paris, 1963. Zbl 0137.02001, MR 0171864 |
| Reference:
|
[13] Goodearl K.R.: Partially Ordered Abelian Groups with Interpolation.Math. Surveys and Monographs No 20, Amer. Math. Soc., Providence, Rhode Island, 1986. Zbl 0589.06008, MR 0845783 |
| Reference:
|
[14] Gudder S., Pulmannová S.: Representation theorem for convex effect algebras.Comment. Math. Univ. Carolinae 39 (1998), 645-659. MR 1715455 |
| Reference:
|
[15] Gudder S.P. et all.: Convex and linear effect algebras.Rep. Math. Phys. 44 (???), 359-379. Zbl 0956.46002, MR 1737384 |
| Reference:
|
[16] Kôpka F., Chovanec F.: D-posets.Math. Slovaca 44 (1994), 21-34. MR 1290269 |
| Reference:
|
[17] Ludwig G.: Foundations of Quantum Mechanics.Springer-Verlag, New York, 1983. Zbl 0574.46057, MR 0690770 |
| Reference:
|
[18] Mundici D.: Interpretations of AF C*-algebras in Lukasziewicz sentential calculus.J. Funct. Anal. Appl. 65 (1986), 15-63. MR 0819173 |
| Reference:
|
[19] Pulmannová S.: Effect algebras with the Riesz decomposition property and AF C*-algebras.Found. Phys. 29 (1999), 1389-1400. MR 1739751 |
| Reference:
|
[20] Ravindran K.: On a structure theory of effect algebras.PhD Thesis, Kansas State University, Mahattan Kansas, 1996. |
| Reference:
|
[21] Wyler O.: Clans.Compositio Math. 17 (1966/67), 172-189. MR 0197368 |
| . |
