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2006 | 26 | 1 | 85-109
Tytuł artykułu

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

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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.
Twórcy
  • University of Potsdam, Institute of Mathematics, Am Neuen Palais, 14415 Potsdam, Germany
  • 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.
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Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1106
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