Logics that are generated by idempotents
type: Item
instance of: scholarly article
title: Logics that are generated by idempotents
zbMATH Open document ID: 1060.15018
author: František Katrnoška
published in: Lobachevskii Journal of Mathematics
publication date: 2004-11-26T00:00:00Z
full work available at URL: kar.html
review text: The idempotence properties of the rings of square matrices are studied. A series of special definitions is given (a logic or an orthomodular coset, orthomodular lattice, a subset of logic, a Boolean subalgebra, a generalized \(R\)-Latin square, a \(R\)-circulant). The generalized theorem which represents one of the cases concerning the characteristics of the logic of idempotents is proved [cf. \textit{V. V. Kalinin}, Algebra Logika 15, 535--557 (1976; Zbl 0377.06003); \textit{F. Katrnoška}, Logics and states of physical systems (in Czech). Thesis, Czech Technical University, Prague (1980); \textit{J. Flachsmeyer}, Topology and measure III, Proc. Conf, Vitte/Hiddensee 1980, Part 1, 65--73 (1982; Zbl 0536.06002)]. \(R\)-circulant matrices in the framework of the ring \(R\) are introduced and some consequences for the logic of idempotents of the corresponding rings are considered. Some examples are indicated. Particularly, the connection between rings of \(2\times 2\)-matrices and spin matrices is briefly discussed.
Mathematics Subject Classification ID: 15B33
Mathematics Subject Classification ID: 16S50
Mathematics Subject Classification ID: 06C15
zbMATH DE Number: 2119177
zbMATH Keywords: ring of matrices
zbMATH Keywords: ring with identity
zbMATH Keywords: idempotents
zbMATH Keywords: orthomodular coset
zbMATH Keywords: projectors of a ring
zbMATH Keywords: \(R\)-circulant matrices
zbMATH Keywords: spin matrices
reviewed by: A. A. Bogush
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2119177