Note on logics of idempontents

• Autorzy: Katrnoška F.
• Języki publikacji: EN

Abstrakty

EN

The main result of this paper is the characterization of certain logics of idempotents by Boolean semirings. Moreover some interesting examples are likewise added.

Słowa kluczowe

EN

idempotents; monoid; pasting; ring with identity; semigroup

PL

idempotentność; monoidy; półgrupy

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2004
• Tom: Vol. 37, nr 2
• Strony: 267--274
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Katrnoška F.

• Institute of Chemical Technology, Department of Mathematics, Technická 5, 16628 Prague 6, Czech Republic

Bibliografia

• [1] G. Birkhoff, Lattice Theory, Amer. Math. Soc. Providence, Rhode Island (1973).
• [2] J. Flachsmeyer, Note on orthocomplemented posets, Proc. Conf. Topology and Measure, Greifswald (1982), 65-75.
• [3] A. L. Foster, The idempotent elements of a commutative ring form a Boolean algebra ring duality and transformation theory, Duke Math. J. 12 (1945), 143.
• [4] V. V. Kalinin, Orthomodular posets with dimension, (in Russian), Algebra and Logic, 15, 5 (1976), 535-557.
• [5] F. Katrnoška, Logics and states of physical systems (in Czech), Thesis, Institute of Chemical Technology, Prague (1980).
• [6] F. Katrnoška, Logics of Idempotents of Rings, Topology, Measure and Fractals, Vol. 66, Akad. Verlag, Berlin (1992), 131-136.
• [7] F. Katrnoška, Logics that are generated by idempotents, submitted.
• [8] G. Lallement, Semigroups and Combinatorial Applications, J. Wiley, New York, Chichester, Brisbane, Toronto (1979).
• [9] D. Ch. Muštari, Logics of projectors in Banach spaces (in Russian), Izv. Vuzov Matematika 8 (1989), 44-52.
• [10] M. Navara, V. Rogalewicz, The pasting constructions for orthomodular posets, Math. Nachr. 154 (1991), 157-168.
• [11] P. Pták, S. Pulmannová, Orthomodular Structures in Quantum Logics, Kluwer Acad. Publ., Dordrecht (1991).
• [12] S. Pulmannová, Automorphisms of orthomodular posets, Atti Sem. Mat. Fis. Univ. Modena XLIV (1996), 415-425.
• [13] V. Rogalewicz, Any orthomodular poset is a pasting of Boolean algebras, Comment. Math. Univ. Carolinae 29 (1988), 557-558.
• [14] O. Steinfeld, About the structure theorems in semirings (in German), Acta Math. Acad. Sci. Hung. 10 (1959), 149-155.
• [15) N. V. Subrahmanyam, Boolean semirings, Math. Ann. 148 (1962), 396-401.
• [16] K. Svozil, Quantum Logic, Springer, Berlin/Heidelberg (1998).