Czasopismo
Tytuł artykułu
Autorzy
Treść / Zawartość
Pełne teksty:
Warianty tytułu
Języki publikacji
Abstrakty
A method is presented for proving primality and functional completeness theorems, which makes use of the operation-relation duality. By the result of Sierpiński, we have to investigate relations generated by the two-element subsets of $A^{k}$ only. We show how the method applies for proving Słupecki's classical theorem by generating diagonal relations from each pair of k-tuples.
Słowa kluczowe
Kategorie tematyczne
Rocznik
Tom
Numer
Strony
5-11
Opis fizyczny
Daty
wydano
2001
otrzymano
1998-02-09
poprawiono
2000-11-06
poprawiono
2001-03-05
Twórcy
autor
- Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, H-6720 Szeged, Hungary
Bibliografia
- [1] K.A. Baker and A.F. Pixley, Polynomial Interpolation and the Chinese Remainder Theorem for Algebraic Systems, Math. Z. 143 (1975), 165-174.
- [2] V.G. Bodnarcuk, L.A. Kaluznin, V.N. Kotov, and B.A. Romov, Galois theory for Post algebras, I and II (Russian), Kibernetika (Kiev) 5 (1969), no. 3 p. 1-10 and no. 5, p. 1-9.
- [3] B. Csákány, Homogeneous algebras are functionally complete, AlgebraUniversalis 11 (1980), 149-158.
- [4] A.L. Foster, An existence theorem for functionally complete universalalgebras, Math. Z. 71 (1959), 69-82.
- [5] E. Fried and A.F. Pixley, The dual discriminator function in universalalgebra, Acta Sci. Math. (Szeged) 41 (1979), 83-100.
- [6] D. Geiger, Closed systems of functions and predicates, Pacific J. Math. 27 (1968), 95-100.
- [7] Th. Ihringer, Allgemeine Algebra, Teubner-Verlag, Stuttgart 1993.
- [8] S.W. Jablonski and O.B. Lupanow, (eds.), Diskrete Mathematik und mathematische Fragen der Kybernetik, Akademie-Verlag, Berlin 1980.
- [9] P.H. Krauss, On primal algebras, Algebra Universalis 2 (1972), 62-67.
- [10] P.H. Krauss, On quasi primal algebras, Math. Z. 134 (1973), 85-89.
- [11] R. Pöschel and L.A. Kaluznin, Funktionen- und Relationenalgebren, Deutschen Verlag der Wissenschaften, Berlin 1979.
- [12] W. Sierpiński, Sur les fonctions de plusieurs variables, Fund. Math. 33 (1945), 169-173.
- [13] J. Słupecki, Completeness criterion for systems of many-valued propositional calculus (in Polish), C.R. des Séances de la Societé des Sciences et des Lettres de Varsovie Cl. II 32 (1939), 102-109., (English transl.: Studia Logica 30 (972), 153-157.
- [14] Á. Szendrei, Clones in Universal Algebra, Les Presses de l'Université de Montréal, Montreal 1986.
- [15] H. Werner, Discriminator-Algebras, Akademie-Verlag, Berlin 1978.
- [16] H. Werner, Eine Characterisierung funktional vollstandiger Algebren, Arch. Math. (Basel) 21 (1970), 381-385.
- [17] S.V. Yablonski, Functional construction in the k-valued logic (Russian), Trudy Math. Inst. Steklov 51 (1958), 5-142.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1022