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2012 | 32 | 1 | 101-114
Tytuł artykułu

On sets related to maximal clones

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EN
Abstrakty
EN
For an arbitrary h-ary relation ρ we are interested to express n-clone Polⁿρ in terms of some subsets of the set of all n-ary operations Oⁿ(A) on a finite set A, which are in general not clones but we can obtain Polⁿρ from these sets by using intersection and union. Therefore we specify the concept a function preserves a relation and moreover, we study the properties of this new concept and the connection between these sets and Polⁿρ. Particularly we study $R_{a̲,b}^{n,k}$ for arbitrary partial order relations, equivalence relations and central relations.
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Twórcy
autor
  • Department of Mathematics Gadjah Mada University, Yogyakarta Indonesia 55281
  • Institute of Mathematics Potsdam University, Potsdam Germany
Bibliografia
  • [1] A. Fearnley, Clones on Three Elements Preserving a Binary Relation, Algebra Universalis 56 (2007) 165-177. doi: 10.1007/s00012-007-1985-5
  • [2] Á. Szendrei, Clones in Universal Algebra (Les Presses de L' Université de Montréal, 1986).
  • [3] I.G. Rosenberg, Über die Funktionale Vollständigkeit in den Mehrwertigen Logiken, Rozpravy Ćeskoslovenské Akad. véd, Ser. Math. Nat. Sci. 80(1970) 3-93
  • [4] K. Denecke, D. Lau, R. Pöschel and D. Schweigert, Hyperidentities, Hyperequational Classes and Clone Congruences, Contributions to General Algebra 7, Verlag Hölder-Pichler-Tempsky, Wien (1991) 97-118
  • [5] K. Denecke and S.L. Wismath, Hyperidentities and Clones (Gordon and Breach Science Publisher, 2000).
  • [6] K. Denecke and S.L. Wismath, Universal Algebra and Applications in Theoretical Computer Science (Chapman and Hall, 2002).
  • [7] K. Denecke and Y. Susanti, Semigroups of n-ary Operations on Finite Sets, in: Proceedings of International Conference on Algebra on Algebra 2010 Advances in Algebraic Structures, W. Hemakul, S. Wahyuni and P.W. Sy(Ed(s)), (World Scientific, 2012) 157-176. doi: 10.1142/9789814366311_0011
  • [8] K. Denecke and Y. Susanti, On Sets Related to Clones of Quasilinear Operations, in: Proceedings of the 6th SEAMS-GMU International Conference on Mathematics and Its Application 2011, S. Wahyuni, I.E. Wijayanti and D. Rosadi (Ed(s)), (University of Gadjah Mada, 2012) 145-158
  • [9] R. Butkote and K. Denecke, Semigroup Properties of Boolean Operations, Asian-Eur. J. Math. 1(2008) 157-176
  • [10] R. Butkote, Universal-algebraic and Semigroup-theoretical Properties of Boolean Operations (Dissertation Universität Potsdam, 2009).
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmal_1190
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