Abstract
An amalgamation of bounded involution posets over a strictly directed graph is introduced and states on this amalgamation are studied. We introduce conditions under which the amalgamation induces a structure that is of the same type as that of the amalgamated structures. We also study circumstances under which common properties of the state spaces (such as unital, full, and strongly order determining) of the amalgamated structures are inherited by the amalgamation.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Al-Agha, K., and Greechie, R. (2003). On the order dimension for involution posets. Research Report No. 2003-01, Louisiana Tech University.
Greechie, R. (1971). Orthomodular lattices admitting no states. Journal of Combinatorial Theory 10(2). 119–132
Kalmbach, G. (1983). Orthomodular Lattices, Academic Press, London.
Author information
Authors and Affiliations
Corresponding author
Additional information
In memory of Günter Bruns.
Rights and permissions
About this article
Cite this article
Al-Agha, K.J., Greechie, R.J. States on Orthomodular Amalgamations Over Trees. Int J Theor Phys 45, 263–275 (2006). https://doi.org/10.1007/s10773-005-9020-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10773-005-9020-0