JP Journal of Algebra, Number Theory and Applications
Volume 46, Issue 2, Pages 153 - 164
(May 2020) http://dx.doi.org/10.17654/NT046020153 |
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FACTORISABLE MONOID OF LINEAR HYPERSUBSTITUTIONS FOR ALGEBRAIC SYSTEMS OF TYPE ((n), (m))
Dawan Chumpungam and Sorasak Leeratanavalee
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Abstract: An algebra is a structure of a nonempty set together with a sequence of operations defined on this set. An algebraic system is a combination of an algebra and a sequence of relations on the base set of this algebra. The properties of an algebraic system are expressed by terms and formulas. In this paper, we study on the set of all linear hypersubstitutions for algebraic systems of type ((n), (m)). A linear hypersubstitution for algebraic systems of type ((n), (m)) is a mapping which maps an n-ary operation symbol to an n-ary linear term and maps an m-ary relation symbol to an m-ary quantifier free linear formula. The set of all linear hypersubstitutions for algebraic systems of type ((n), (m)) with a binary operation on this set and the identity element forms a monoid. In this paper, we determine the set of all unit-elements of this monoid. We also conclude that this monoid is factorisable. |
Keywords and phrases: algebraic systems, linear hypersubstitution, unit-element, factorisable monoid.
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