Free algebras over a poset in varieties of Łukasiewicz-Moisil algebras

• Autorzy: Figallo Orellano, A. , Gallardo, C.
• Języki publikacji: EN

Abstrakty

EN

A general construction of the free algebra over a poset in varieties finitely generated is given in [8]. In this paper, we apply this to the varieties of Łukasiewicz–Moisil algebras, giving a detailed description of the free algebra over a finite poset (X, ≤), Free n ((X, ≤)). As a consequence of this description, the cardinality of Free n ((X, ≤)) is computed for special posets.

Słowa kluczowe

PL

algebra; zbiór częściowo uporządkowany; poset; algebra Łukasiewicza-Moisila

EN

algebras; free algebras over a poset; Łukasiewicz–Moisil algebras

• Czasopismo: Demonstratio Mathematica
• Rocznik: 2015
• Tom: Vol. 48, nr 3
• Strony: 348--356
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Figallo Orellano, A.

• Departamento de Matemática, Universidad Nacional Del Sur, Argentina,

autor

Gallardo, C.

• Departamento de Matemática, Universidad Nacional Del Sur, Argentina,

Bibliografia

• [1] R. Cignoli, Moisil algebras, Notas de Lógica Matemática No27, Instituto de Matemática, Universidad Nacional del Sur, 1970.
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• [3] S. Burris, H. Sankappanavar, A Course in Universal Algebra, Graduate Texts in Mathematics, 78, Springer-Verlag, New York-Berlin, 1981.
• [4] D. Buşneag, F. Chirteş, LMn-algebra of fractions and maximal LMn-algebra of fractions, Discrete Math. 296(2–3) (2005), 143–165.
• [5] R. Dilworth, Lattices with unique complements, Trans. Amer. Math. Soc. 57 (1945), 123–154.
• [6] G. Georgescu, I. Leustean, A. Popescu, Order convergence and distance on Łukasiewicz–Moisil algebras, J. Mult.-Valued Logic Soft Comput. 12(1–2) (2006), 33–69.
• [7] A. Figallo, Jr., Free algebras over a poset in varieties generated by a finite number of algebras, CLE e-Prints of the Centre for Logic, Vol. 9(3), 2009.
• [8] A. Figallo, Jr. and A. Ziliani, Free algebras over a poset in varieties, Commun. Korean Math. Soc. 26 (2011), 543–549.
• [9] S. Mac Lane, Categories for the Working Mathematician, second ed., Graduate Texts in Mathematics, vol. 5, Springer-Verlag, New York, 1998, xii+314 pp.

Identyfikatory

DOI

10.1515/dema-2015-0024