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

Klaus Denecke; Prakit Jampachon

Discussiones Mathematicae - General Algebra and Applications (2006)

- Volume: 26, Issue: 1, page 85-109
- ISSN: 1509-9415

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topKlaus Denecke, and Prakit Jampachon. "Regular elements and Green's relations in Menger algebras of terms." Discussiones Mathematicae - General Algebra and Applications 26.1 (2006): 85-109. <http://eudml.org/doc/276840>.

@article{KlausDenecke2006,

abstract = {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.},

author = {Klaus Denecke, Prakit Jampachon},

journal = {Discussiones Mathematicae - General Algebra and Applications},

keywords = {term; superposition of terms; Menger algebra; regular element; Green's relations},

language = {eng},

number = {1},

pages = {85-109},

title = {Regular elements and Green's relations in Menger algebras of terms},

url = {http://eudml.org/doc/276840},

volume = {26},

year = {2006},

}

TY - JOUR

AU - Klaus Denecke

AU - Prakit Jampachon

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

JO - Discussiones Mathematicae - General Algebra and Applications

PY - 2006

VL - 26

IS - 1

SP - 85

EP - 109

AB - 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.

LA - eng

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

UR - http://eudml.org/doc/276840

ER -

## References

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- [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. Zbl1015.08005
- [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. Zbl1083.08005
- [5] K. Denecke and P. Jampachon, Clones of Full Terms, Algebra Discrete Math. 4 (2004), 1-11. Zbl1091.08003
- [6] K. Denecke and J. Koppitz, M-solid Varieties of Algebras, Advances in Mathematics, Springer Science+Business Media, Inc., 2006. Zbl1094.08001
- [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. Zbl0113.03904
- [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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