Regular elements and Green's relations in power Menger algebras of terms

• Autorzy: Denecke K. , Glubudom P.
• Języki publikacji: EN

Abstrakty

EN

Sets of terms of type r are called tree languages (see [5]). On sets of tree languages superposition operations can be defined in such a way that the collection of all tree languages of type r forms an abstract clone. Considering only sets of n-ary terms one obtains a Menger algebra (see e.g. [3]). From the superposition operations binary operations on tree languages can be derived. For the corresponding sernigroups of tree languages we study idempotent and regular elements as well as Green's relations L and R.

Słowa kluczowe

EN

Menger algebra; Green's relations; idempotent element; regular element; tree language

PL

algebra Mengera; relacja Green'sa; element idempotentny; element prawidłowy

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2008
• Tom: Vol. 41, nr 1
• Strony: 11--22
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Denecke K.

autor

Glubudom P.

• Universitat Potsdam Fachbereich Mathematik Postfach 601553 14415 Potsdam,, Germany,

Bibliografia

• [1] K. Denecke, S. L. Wismath, Universal Algebra and Applications in Theoretical Computer Science, Chapman & Hall/CRC, Boca Raton, London, New York, Washington, D. C., 2002.
• [2] K. Denecke, P. Glubudom, J. Koppitz, Power Clones and Non-deterministic hypersubstitutions, preprint 2005.
• [3] K. Denecke, P. Glubudom, Generalized Power Menger Algebras and Generalized Nondeterministic Hypersubstitutions, Contributions to General Algebra, Proceedings of the Vienna Conference 2005, Verlag Johaunes Heyn, Klagenfurth, pp. 61-70.
• [4] K. Denecke, P. Glubudom, Green's Quasiorder on Menger Algebras of Terms, Thai Journal of Mathematics, Vol. 4 (2006), number 1: 49-61.
• [5] P. Gecseg, M. Steinby, Tree Languages, in; Handbook of Formal Languages, Vol. 3, Chapter 1, Tree Languages, pp. 1-68, Springer-Verlag 1997.
• [6] K. Denecke, J. Koppitz, M-solid Varieties of Algebras, Advances in Mathematics, Springer-Verlag 2006.
• [7] B. M. Schein, V. S. Trohiinenko, Algebras of multiplace functions, Semigroup Forum Vol. 17 (1979), 1-64.