T-Varieties and Clones of T-terms

Klaus Denecke; Prakit Jampachon

Discussiones Mathematicae - General Algebra and Applications (2005)

  • Volume: 25, Issue: 1, page 89-101
  • ISSN: 1509-9415

Abstract

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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.

How to cite

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Klaus Denecke, and Prakit Jampachon. "T-Varieties and Clones of T-terms." Discussiones Mathematicae - General Algebra and Applications 25.1 (2005): 89-101. <http://eudml.org/doc/287686>.

@article{KlausDenecke2005,
abstract = {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.},
author = {Klaus Denecke, Prakit Jampachon},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {T-quasi constant algebra; T-identity; j-ideal; T-hyperidentity; clone of T-terms; -quasi constant algebra; -identity; -ideal; -hyperidentity; -variety; clone of -terms},
language = {eng},
number = {1},
pages = {89-101},
title = {T-Varieties and Clones of T-terms},
url = {http://eudml.org/doc/287686},
volume = {25},
year = {2005},
}

TY - JOUR
AU - Klaus Denecke
AU - Prakit Jampachon
TI - T-Varieties and Clones of T-terms
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2005
VL - 25
IS - 1
SP - 89
EP - 101
AB - 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.
LA - eng
KW - T-quasi constant algebra; T-identity; j-ideal; T-hyperidentity; clone of T-terms; -quasi constant algebra; -identity; -ideal; -hyperidentity; -variety; clone of -terms
UR - http://eudml.org/doc/287686
ER -

References

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