On MV-algebras of non-linear functions | ||
| Categories and General Algebraic Structures with Applications | ||
| مقاله 10، دوره 6، Speical Issue on the Occasion of Banaschewski's 90th Birthday (I)، فروردین 2017، صفحه 107-120 اصل مقاله (423.98 K) | ||
| نوع مقاله: Research Paper | ||
| نویسندگان | ||
| Antonio Di Nola؛ Giacomo Lenzi* ؛ Gaetano Vitale | ||
| Department of Mathematics, University of Salerno, Via Giovanni Paolo II 132, I-84084 Fisciano (SA), Italy. | ||
| چکیده | ||
| In this paper, the main results are: a study of the finitely generated MV-algebras of continuous functions from the n-th power of the unit real interval I to I; a study of Hopfian MV-algebras; and a category-theoretic study of the map sending an MV-algebra as above to the range of its generators (up to a suitable form of homeomorphism). | ||
| کلیدواژهها | ||
| MV-algebra؛ McNaughton function؛ Hopfian algebra | ||
| مراجع | ||
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[1] Belluce, L.P., Di Nola, A., and Lenzi, G., Hyperfinite MV-algebras, J. Pure Appl. Algebra 217 (2013), 1208-1223. [2] Birkhof G. and Pierce, R., Lattice-ordered rings, An. Acad. Brasil. Ci^enc. 28 (1956), 41-69. [3] Cabrer, L. and Mundici, D., Projective MV-algebras and rational polyhedra, Algebra Universalis 62 (2009), 63-74. [4] Cignoli, R., D'Ottaviano, I., and Mundici, D., Algebraic Foundations of Many-Valued Reasoning", Trends in Logic-Studia Logica Library 7, Springer, 2000. [5] Evans, T., Finitely presented loops, lattices, etc. are hopfian, J. London Math. Soc. 44 (1969), 551-552. [6] Hopf, H., Fundamentalgruppe und zweite Bettische Gruppe (German), Comment. Math. Helv. 14 (1942), 257-309. [7] Loats, J. and Rubin, M., Boolean algebras without nontrivial onto endomorphisms exist in every uncountable cardinality, Proc. Amer. Math. Soc. 72(2) (1978), 346-351. [8] Lyapunov, A.M., The general problem of the stability of motion, Translated by A.T. Fuller from Edouard Davaux's French translation (1907) of the 1892 Russian original, Int. J. Control 55(3) (1992), 531-773. [9] Marra, V. and Spada, L., The dual adjunction between MV-algebras and Tychonof spaces, Studia Logica 100(1-2) (2012), 253-278. [10] Mundici, D., Personal communication. [11] Mundici, D., Advanced Lukasiewicz Calculus and MV-algebras", Trends in Logic-Studia Logica Library 35, Springer, 2011. [12] Mundici, D., Hopfian `-groups, MV-algebras and AF C-algebras, ArXiv:1509.03230. [13] Peano, G., Sur une courbe, qui remplit toute une aire plane, Math. Ann. 36(1) (1890), 157-160. [14] Schoenberg, I.J., Contributions to the problem of approximation of equidistant data by analytic functions, Part A. On the problem of smoothing or graduation. A first class of analytic approximation formulae, Quart. Appl. Math. 4 (1946), 45-99. [15] Schoenberg, I.J., Contributions to the problem of approximation of equidistant data by analytic functions. Part B. On the problem of osculatory interpolation. A second class of analytic approximation formulae, Quart. Appl. Math. 4 (1946), 112-141. [16] Steinberg, B., Private communication. [17] Verhulst, P.F., Recherches mathematiques sur la loi d'accroissement de la population, NouveauxMemoires de l'Academie Royale des Sciences et Belles-Lettres de Bruxelles 18 (1845), 14-54. | ||
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