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

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

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