Geodesic
T-Varieties and Clones of T-terms
Discussiones Mathematicae. General Algebra and Applications, Tome 25 (2005) no. 1, pp. 89-101

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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 T of W_τ(X), the set of all terms of type τ, and consider identities from T×T. Since any variety can be described by one heterogenous algebra, its clone, we are also interested in the corresponding clone-like structure. Identities of the clone of a variety V correspond to M-hyperidentities for certain monoids M of hypersubstitutions. Therefore we will also investigate these monoids and the corresponding M-hyperidentities.
Keywords: T-quasi constant algebra, T-identity, j-ideal, T-hyperidentity, clone of T-terms 
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Denecke, Klaus; Jampachon, Prakit. T-Varieties and Clones of T-terms. Discussiones Mathematicae. General Algebra and Applications, Tome 25 (2005) no. 1, pp. 89-101. http://geodesic.mathdoc.fr/item/DMGAA_2005_25_1_a3/