Partial Algebraic Systems of type (T_n ,(n))

Volume 8, Issue 2, April 2023     |     PP. 62-86      |     PDF (3890 K)    |     Pub. Date: May 31, 2023
DOI: 10.54647/mathematics110401    90 Downloads     151623 Views  

Author(s)

Saofee Busaman, Department of Mathematics and Computer Science, Faculty of Science and Technology, Prince of Songkla University Pattani Campus, 94000 Thailand

Abstract
In this paper, we define the set (CF_(T_n,(n))(X_n))^{A^s} of all n-ary C-formulas on the partial algebraic system A^s=(A;(f^A_i)_i in I,r^A) of type (T_n,(n)) and define the operation R^{n,A} on the set( (W^C_{T_n}(X_n))^{A^s}U(CF_(T_n,(n))(X_n))^{A^s}. After this definition we have a unitary Menger algebra ( ( (W^C_{T_n}(X_n))^{A^s}U(CF_(T_n,(n))(X_n))^{A^s};R^{n,A},x^{A^s}_1,...,x^{A^s}_n) of rank n . Finally, we show that the set of all C-hypersubstitutions for an algebraic system of the type (T_n,(n)) with a binary operation on this set and the identity element forms a monoid.

Keywords
term, unitary Menger algebra of rank n, hypersubstitution.

Cite this paper
Saofee Busaman, Partial Algebraic Systems of type (T_n ,(n)) , SCIREA Journal of Mathematics. Volume 8, Issue 2, April 2023 | PP. 62-86. 10.54647/mathematics110401

References

[ 1 ] F. Börner, Varieties of Partial Algebras, Beiträge zur Algebra und Geometrie, 37(2),(1996), 259-287.
[ 2 ] P. Burmeister, A model Theoretic Oriented Approach to Partial Algebras. Introduction to Theory and Application of Partial Algebras-Part I, Akademie-Verlag Berlin, (1986), 1-319.
[ 3 ] P. Burmeister, Lecture Notes on Universal Algebra-Many-Sorted Partial Algebras, (2002), 1-204.
[ 4 ] S. Busaman, Hyperequational Theory for partial algebras, Ph.D.Thesis, Universitat Potsdam, (2006), 1-131.
[ 5 ] S. Busaman, Unitary Menger algebra of C-quantifier free formulas of type , Asian-European Journal of Mathematics, Vol.14, No.4, DOI:10.1142/S1793557121500509, (2021), 1-20.
[ 6 ] W. Craig, Near equational and equational systems of logic for partial functions I, The Journal of Symbolic Logic, 54(1989), 795-827,.
[ 7 ] K. Denecke and J. Koppitz, M-solid Varieties of Algebras, Springer-Verlag, (2006), 1-341.
[ 8 ] K. Denecke, D. Lau, R. Pöschel and D. Schweigert, Hyperidentities, hyperequational classes and clone congruences, Contributions to General Algebra, Vol. 7, Verlag Hölder-Pichler-Tempsky, Wien, (1991), 97-118.
[ 9 ] A.I. Mal'cev, Algebraic Systems, Akademie-Verlag, Berlin, (1973), 1-317.
[ 10 ] D. Phusanga, Derived Algebric Systems, Ph.D.Thesis, Universität Potsdam, (2013), 1-81.
[ 11 ] D. Welke, Hyperidentitäten partieller Algebren, Ph.D.Thesis, Universität Potsdam, (1996), 1-104.