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

• Autorzy: Klaus Denecke , Prakit Jampachon
• 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

term; superposition of terms; Menger algebra; regular element; Green's relations

Kategorie tematyczne

• 08A40: Operations, polynomials, primal algebras
• 08A35: Automorphisms, endomorphisms
• 08A70: Applications of universal algebra in computer science

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae - General Algebra and Applications
• Rocznik: 2006
• Tom: 26
• Numer: 1
• Strony: 85-109

Daty

wydano

2006

otrzymano

2005-07

poprawiono

2005-08

Twórcy

autor

Klaus Denecke

• University of Potsdam, Institute of Mathematics, Am Neuen Palais, 14415 Potsdam, Germany

autor

Prakit Jampachon

• 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.

Identyfikatory

DOI

10.7151/dmgaa.1106