Research ArticleOpen AccessGoogle Scholar indexed
The Localization of Commutative Bounded BCK-Algebras
Faculty of Mathematics and Computer Science, University of Craiova, Craiova, Romania
Faculty of Mathematics and Computer Science, University of Craiova, Craiova, Romania
- 1 Faculty of Mathematics and Computer Science, University of Craiova, Craiova, Romania
- 2 Faculty of Mathematics and Computer Science, University of Craiova, Craiova, Romania
Advances in Pure Mathematics·Volume 01 (2011)·Pages 367–377·Published 24 November 2011·DOI10.4236/apm.2011.16066
Copy link · social · email
Abstract
In this paper we develop a theory of localization for bounded commutative BCK-algebras. We try to extend some results from the case of commutative Hilbert algebras (see [1]) to the case of commutative BCK-alge- bras.
KeywordsBCK-AlgebraCommutative BCK-AlgebraAlgebra of FractionsMaximal Algebra of Quotients∨-Closed SystemTopologyLocalization Algebra
- D. Piciu and C. Busneag, “The Localization of Commutative (Unbounded) Hilbert Algebras,” Mathematical Reports, Vol. 12, No. 3, 2010, pp. 285-300.
- Y. Imai and K. Iséki, “On Axiom Systems of Propositional Calculi XIV,” Proceedings of the Japan Academy, Vol. 42, No. 1, 1966, pp. 19-22. doi:10.3792/pja/1195522169
- A. N. Prior, “Formal logic, 2nd Ed,” Oxford, 1962.
- G. Georgescu, “F-Multipliers and the Localization of Distributive Lattices,” Algebra Universalis, Vol. 21, No. 2-3, 1985, pp. 181-197. doi:10.1007/BF01188055
- S. Rudeanu, “Localizations and Fractions in Algebra of Logic,” Journal of Multi-Valued Logic & Soft Computing, Vol. 16, No. 3-5, 2010, pp. 465-467.
- R. Cignoli and A. Torens, “Glivenko Like Theorems in Natural Expansions of BCK-Logic,” Mathematical Logic Quarterly, Vol. 50, No. 2, 2004, pp. 111-125. doi:10.1002/malq.200310082
- J. Gispert and A. Torrens, “Boolean Representation of Bounded BCK-Algebras,” Soft Computing, Vol. 12, No. 10, 2008, pp. 941-954. doi:10.1007/s00500-007-0261-0
- A. Iorgulescu, “Algebras of Logic as BCK-Algebras,” ASE, Bucharest, 2008.
- K. Iséki and S. Tanaka, “An Introduction to the Theory of BCK-Algebras,” Mathematica Japonica, Vol. 23, No. 1, 1978, pp. 1-25.
- F. M. G. Olmedo and A. J. R. Salas, “Negation and BCK- Algebras,” Mathematical Logic Quarterly, Vol. 49, No. 4, 2003, pp. 336-346. doi:10.1002/malq.200310035
- J. Schmid, “Multipliers on Distributive Lattices and Rings of Quotients,” Houston Journal of Mathematics, Vol. 6, No. 3, 1980, pp. 401-425.
- J. Schmid, “Distributive Lattices and Rings of Quotients,” Colloquia Mathematica Societatis János Bolyai, Vol. 33, Szeged, Hungary, 1980.
- J. Lambek, “Lectures on Rings and Modules,” Blaisdell Publishing Company, New York, 1966.
- H. Cornish, “The Multiplier Extension of a Distributive Lattice,” Journal of Algebra, Vol. 32, No. 2, 1974, pp. 339-355. doi:10.1016/0021-8693(74)90143-4
- R. Balbes and Ph. Dwinger, “Distributive Lattices,” University of Missouri Press, Columbia, 1974.
- N. Popescu, “Abelian Categories with Applications to Rings and Modules,” Academic Press, New York, 1973.
- B. Strenstr?m, “Platnes and Localization over Monoids,” Mathematische Nachrichten, Vol. 48, No. 1-6, 1971, pp. 315-334. doi:10.1002/mana.19710480124