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2005 | 25 | 1 | 89-101
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T-Varieties and Clones of T-terms

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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.
  • University of Potsdam, Institute of Mathematics, Am Neuen Palais, 14415 Potsdam, Germany
  • KhonKaen University, Department of Mathematics, KhonKaen, 40002 Thailand
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