Comparability groups

• Autorzy: Foulis D. , Foulis D.
• Języki publikacji: EN

Abstrakty

EN

A comparability group is a unital group with a compression base and with the general comparability property. The additive group of self-adjoint elements in a von Neumann algebra, and any Dedekind sigma-complete lattice-ordered abelian group with order unit are examples of comparability groups. We develop the basic theory of comparability groups, and show that an archimedean comparability group with the Rickart projection property can be embedded in a partially ordered rational vector space the elements of which admit a rational spectral resolution.

Słowa kluczowe

EN

abelian group; compression base; absolute value; orthomodular poset; orthomodular lattice; divisible hull; spectral decomposition

PL

grupa abelowa; struktury ortomodularne; powłoki podzielne; rozkłady spektralne; bezwzględna większość

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2006
• Tom: Vol. 39, nr 1
• Strony: 15--32
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Foulis D.

autor

Foulis D.

• 1 Sutton Court Amherst, MA 01002, USA,

Bibliografia

• [1] M. K. Bennett and D. J. Foulis, Interval and scale effect algebras, Adv. Appl. Math. 19 (1997) 200-215.
• [2] D. J. Foulis, MV and Heyting effect algebras, Found. Physics 30, No. 10 (2000) 1687-1706.
• [3] D. J. Foulis, Compressible groups, Math. Slovaca 53, No. 5 (2003) 433-455.
• [4] D. J. Foulis, Compressions on partially ordered abelian groups, Proc. Amer. Math. Soc. 132 (2004) 3581-3587.
• [5] D. J. Foulis, Spectral resolution in a Rickart comgroup, Rep. Math. Phys. 54, No. 2 (2004) 319-340.
• [6] D. J. Foulis, Compressible groups with general comparability, to appear in Math. Slovaca.
• [7] D. J. Foulis, Compression bases in unital groups, to appear in Internat. J. Theor. Phys.
• [8] K. R. Goodearl, Partially Ordered Abelian Groups with Interpolation, A.M.S. Mathematical Surveys and Monographs, No. 20, American Mathematical Society, Providence, RI, 1986.
• [9] R. J. Greechie, D. J. Foulis and S. Pulmannová. The center of an effect algebra, Order 12 (1995), 91-106.
• [10] S. P. Gudder, Examples, problems, and results in effect algebras, Internat. J. Theor. Phys. 35 (1996) 2365-2376.
• [11] P. Pták and S. Pulmannová, Orthomodular Structures as Quantum Logics, Kluwer, Dordrecht/Boston/London, 1991.