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## Discussiones Mathematicae - General Algebra and Applications

2006 | 26 | 1 | 85-109
Tytuł artykułu

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

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Defining an (n+1)-ary superposition operation $S^n$ on the set $W_{τ}(X_n)$ of all n-ary terms of type τ, one obtains an algebra $n-clone τ := (W_{τ}(X_n); S^n, x_1, ..., x_n)$ of type (n+1,0,...,0). The algebra n-clone τ is free in the variety of all Menger algebras ([9]). Using the operation $S^n$ there are different possibilities to define binary associative operations on the set $W_{τ}(X_n)$ and on the cartesian power $W_{τ}(X_n)^n$. In this paper we study idempotent and regular elements as well as Green's relations in semigroups of terms with these binary associative operations as fundamental operations.
Słowa kluczowe
EN
Kategorie tematyczne
Rocznik
Tom
Numer
Strony
85-109
Opis fizyczny
Daty
wydano
2006
otrzymano
2005-07
poprawiono
2005-08
Twórcy
autor
• University of Potsdam, Institute of Mathematics, Am Neuen Palais, 14415 Potsdam, Germany
autor
• KhonKaen University, Department of Mathematics, KhonKaen, 40002 Thailand
Bibliografia
• [1] K. Denecke, Stongly Solid Varieties and Free Generalized Clones, Kyungpook Math. J. 45 (2005), 33-43.
• [2] K. Denecke and S.L. Wismath, Universal Algebra and Applications in Theoretical Computer Science, Chapman & Hall/CRC, Boca Raton, London, New York, Washington, D.C., 2002.
• [3] K. Denecke and S.L. Wismath, Complexity of Terms, Composition and Hypersubstitution, Int. J. Math. Math. Sci. 15 (2003), 959-969.
• [4] K. Denecke and P. Jampachon, N-solid varieties and free Menger algebras of rank n, East-West Journal of Mathematics 5 (1) (2003), 81-88.
• [5] K. Denecke and P. Jampachon, Clones of Full Terms, Algebra Discrete Math. 4 (2004), 1-11.
• [6] K. Denecke and J. Koppitz, M-solid Varieties of Algebras, Advances in Mathematics, Springer Science+Business Media, Inc., 2006.
• [7] J.M. Howie, Fundamenntals of Semigroup Theory, Oxford Science Publications, Clarendon Press, Oxford 1995.
• [8] K. Menger, The algebra of functions: past, present, future, Rend. Mat. 20 (1961), 409-430.
• [9] B.M. Schein and V.S. Trohimenko, Algebras of multiplace functions, Semigroup Forum 17 (1979), 1-64.
• [10] V.S. Trohimenko, v-regular Menger algebras, Algebra Univers. 38 (1997), 150-164.
Typ dokumentu
Bibliografia
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