It is shown that divisible effect algebras are in one-to-one correspondence with unit intervals in partially ordered rational vector spaces.
@article{119238, author = {Sylvia Pulmannov\'a}, title = {Divisible effect algebras and interval effect algebras}, journal = {Commentationes Mathematicae Universitatis Carolinae}, volume = {42}, year = {2001}, pages = {219-236}, zbl = {1052.03040}, mrnumber = {1832142}, language = {en}, url = {http://dml.mathdoc.fr/item/119238} }
Pulmannová, Sylvia. Divisible effect algebras and interval effect algebras. Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001) pp. 219-236. http://gdmltest.u-ga.fr/item/119238/
Free sums of groups and their generalizations. An analysis of the associative law, Amer. J. Math. 41 (1949), 706-742. (1949) | MR 0030953 | Zbl 0033.34504
Interval and scale effect algebras, Adv. in Appl. Math. 19 (1997), 200-215. (1997) | MR 1459498 | Zbl 0883.03048
Groupes et Anneaux Réticulés, Springer-Verlag, Berlin-Heidelberg-New York, 1977. | MR 0552653 | Zbl 0384.06022
Fundamentals of fuzzy probability theory, Internat. J. Theoret. Phys. 35 (1996), 2229-2244. (1996) | MR 1423402 | Zbl 0872.60003
Operational Quantum Physics, Springer-Verlag, Berlin, 1995. | MR 1356220
Algebraic Foundations of Many-valued Reasoning, Kluwer Academic Publ., Dordrecht 2000. | MR 1786097 | Zbl 0937.06009
Quantum logic, in Handbook of Philosophical logic, Eds. D. Gabbay, F. Guenthner, Kluwer Acad. Publ., Dordrecht, to appear. | MR 1818789 | Zbl 0969.03070
New Trends in Quantum Structures, Kluwer Acad. Publ., Dordrecht, 2000. | MR 1861369
Weakly divisible MV-algebras and product, J. Math. Anal. Appl. 234 (1999), 208-222. (1999) | MR 1694841
Effect algebras and unsharp quantum logics, Found. Phys. 37 (1994), 1325-1346. (1994) | MR 1304942
Sums and products of interval effect algebras, Internat. J. Theoret. Phys. 33 (1994), 2119-2136. (1994) | MR 1311152
Partially Ordered Algebraic Systems, Pergamon Press, Oxford-London-New York-Paris, 1963. | MR 0171864 | Zbl 0137.02001
Partially Ordered Abelian Groups with Interpolation, Math. Surveys and Monographs No 20, Amer. Math. Soc., Providence, Rhode Island, 1986. | MR 0845783 | Zbl 0589.06008
Representation theorem for convex effect algebras, Comment. Math. Univ. Carolinae 39 (1998), 645-659. (1998) | MR 1715455
Convex and linear effect algebras, Rep. Math. Phys. 44 (???), 359-379. (???) | MR 1737384 | Zbl 0956.46002
D-posets, Math. Slovaca 44 (1994), 21-34. (1994) | MR 1290269
Foundations of Quantum Mechanics, Springer-Verlag, New York, 1983. | MR 0690770 | Zbl 0574.46057
Interpretations of AF C*-algebras in Lukasziewicz sentential calculus, J. Funct. Anal. Appl. 65 (1986), 15-63. (1986) | MR 0819173
Effect algebras with the Riesz decomposition property and AF C*-algebras, Found. Phys. 29 (1999), 1389-1400. (1999) | MR 1739751
On a structure theory of effect algebras, PhD Thesis, Kansas State University, Mahattan Kansas, 1996.
Clans, Compositio Math. 17 (1966/67), 172-189. (1966/67) | MR 0197368