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Partial Menger algebras and their weakly isomorphic representation.
- Source :
- Mathematics Open; 2022, Vol. 1, p1-15, 15p
- Publication Year :
- 2022
-
Abstract
- As generalization of semigroups, Karl Menger introduced in the 1940th algebras of multiplace operations. Such algebras satisfy the superassociative law, a generalization of the associative law. Menger algebras are defined as models of this superassociative law. Cayley's theorem for semigroups says that any model of the associative law is isomorphic to a transformation semigroup. R. M. Dicker proved in 1963 that every Menger algebra of rank n is isomorphic to a Menger algebra of n -ary operations on some set. The composition of terms in which each variable occurs at most r -times, so-called r -terms, leads to partial algebras where the superassociative law is satisfied as a weak identity. In this paper, we introduce the concepts of a partial Menger algebra, a unitary partial Menger algebra and of a generalized partial Menger algebra. We prove that r -terms of some type form a generalized partial Menger algebra with infinitely many nullary operations. Using weak identities and weak isomorphisms, Dicker's result will be extended to partial Menger algebras and to unitary partial Menger algebras. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 28110072
- Volume :
- 1
- Database :
- Complementary Index
- Journal :
- Mathematics Open
- Publication Type :
- Academic Journal
- Accession number :
- 172959547
- Full Text :
- https://doi.org/10.1142/S2811007222500031