Geodesic
Logics that are generated by idempotents
Lobachevskii journal of mathematics, Tome 15 (2004), pp. 11-19.

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The main result of this paper is the generalization of the theorem which represents one of the generally accepted cases concerning the characterization of the logic of idempotents (see [5], [6], [7]). If $R$ is a ring then the $R$-circulant matrices are introduced and some consequences for the logics of idempotents of the corresponding rings. Some convenient examples are added as well. Certain results of this paper may find applications in the foundation of quantum theory.
Keywords: ring and *ring with identity, idempotents, projectors of a *ring. 
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F. Katrnoška. Logics that are generated by idempotents. Lobachevskii journal of mathematics, Tome 15 (2004), pp. 11-19. http://geodesic.mathdoc.fr/item/LJM_2004_15_a1/

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