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Transactions of the American Mathematical Society

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A representation theorem for measurable relation algebras with cyclic groups


Authors: Hajnal Andréka and Steven Givant
Journal: Trans. Amer. Math. Soc. 371 (2019), 7175-7198
MSC (2010): Primary 03G15, 20A15
DOI: https://doi.org/10.1090/tran/7566
Published electronically: February 21, 2019
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Abstract: A relation algebra is measurable if the identity element is a sum of atoms, and the square $ x;1;x$ of each subidentity atom $ x$ is a sum of non-zero functional elements. These functional elements form a group $ G_x$. We prove that a measurable relation algebra in which the groups $ G_x$ are all finite and cyclic is completely representable. A structural description of these algebras is also given.


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Additional Information

Hajnal Andréka
Affiliation: Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Reáltanoda utca 13-15, Budapest, 1053 Hungary
Email: andreka.hajnal@renyi.mta.hu

Steven Givant
Affiliation: Mills College, 5000 MacArthur Boulevard, Oakland, California 94613
Email: wang@mills.edu

DOI: https://doi.org/10.1090/tran/7566
Received by editor(s): October 17, 2017
Received by editor(s) in revised form: December 31, 2017, January 24, 2018, and February 23, 2018
Published electronically: February 21, 2019
Additional Notes: This research was partially supported by Mills College and the Hungarian National Foundation for Scientific Research, Grants T30314 and T35192.
Article copyright: © Copyright 2019 American Mathematical Society