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The monoid of generalized hypersubstitutions of type τ = (n)

Wattapong Puninagool, Sorasak Leeratanavalee (2010)

Discussiones Mathematicae - General Algebra and Applications

A (usual) hypersubstitution of type τ is a function which takes each operation symbol of the type to a term of the type, of the same arity. The set of all hypersubstitutions of a fixed type τ forms a monoid under composition, and semigroup properties of this monoid have been studied by a number of authors. In particular, idempotent and regular elements, and the Green’s relations, have been studied for type (n) by S.L. Wismath. A generalized hypersubstitution of type τ=(n) is a mapping σ which takes...

The positive and generalized discriminators don't exist

A.G. Pinus (2000)

Discussiones Mathematicae - General Algebra and Applications

In this paper it is proved that there does not exist a function for the language of positive and generalized conditional terms that behaves the same as the discriminator for the language of conditional terms.

The Słupecki criterion by duality

Eszter K. Horváth (2001)

Discussiones Mathematicae - General Algebra and Applications

A method is presented for proving primality and functional completeness theorems, which makes use of the operation-relation duality. By the result of Sierpiński, we have to investigate relations generated by the two-element subsets of A k only. We show how the method applies for proving Słupecki’s classical theorem by generating diagonal relations from each pair of k-tuples.

The submaximal clones on the three-element set with finitely many relative R-classes

Erkko Lehtonen, Ágnes Szendrei (2010)

Discussiones Mathematicae - General Algebra and Applications

For each clone C on a set A there is an associated equivalence relation analogous to Green's R-relation, which relates two operations on A if and only if each one is a substitution instance of the other using operations from C. We study the maximal and submaximal clones on a three-element set and determine which of them have only finitely many relative R-classes.

T-Varieties and Clones of T-terms

Klaus Denecke, Prakit Jampachon (2005)

Discussiones Mathematicae - General Algebra and Applications

The aim of this paper is to describe how varieties of algebras of type τ can be classified by using the form of the terms which build the (defining) identities of the variety. There are several possibilities to do so. In [3], [19], [15] normal identities were considered, i.e. identities which have the form x ≈ x or s ≈ t, where s and t contain at least one operation symbol. This was generalized in [14] to k-normal identities and in [4] to P-compatible identities. More generally, we select a subset...

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