Abstract
Orthomodular lattices and posets, orthoalgebras, and D-posets are all examples of partial Abelian semigroups. So, too, are the event structures of test spaces. The passage from an algebraic test space to its logic (an orthoalgebra) is an instance of a general construction involving a partial Abelian semigroupL and a distinguished subsetM \( \subseteq \) L such that perspectivity with respect toM is a congruence onL. The quotient ofL by such a congruence is always a cancellative, unital PAS, and every such PAS arises canonically as such a quotient.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Dvurecenskij, A., and Pulmannová, S. (1994).Reports on Mathematical Physics,34, 151–170.
Foulis, D. J., Greechie, R. J., and Rüttimann, G. T. (1992).International Journal of Theoretical Physics,31, 789–807.
Foulis, D. J., and Bennett, M. K. (1994). Effect algebras and unsharp quantum logics,Foundations of Physics,24, 1325–1346.
Kôpka, F., and Chovanec, F. (1994).Mathematica Slovaca,44, 21–34.
Pulmannová, S., and Wilce, A. (1994). Representations of D-posets, preprint.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Wilce, A. Partial Abelian semigroups. Int J Theor Phys 34, 1807–1812 (1995). https://doi.org/10.1007/BF00676295
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00676295