The pre-clone of a variety

• Autorzy: Denecke K. , Wismath S.
• Języki publikacji: EN

Abstrakty

EN

Clones are sets of operations on a given base set which are closed under superposition of operations and which contain all the projection operations. A clone can be regarded as a heterogeneous or multi-based algebra, consisting of universe sets of n-ary operations, for n > 1, with the superposition operations Snm, for n,m > 1. Such an algebra is called a Menger system. For a fixed n, a set of n-ary operations with the (n + 1)-ary superposition operation Sn forms a homogeneous algebra called a Menger algebra of rank n. These structures can also be defined on sets of term operations of a fixed type r. The set of all terms of type r which contain at least one operation symbol forms such a clone-like structure which we call the pre-clone of type r. We determine a generating system for this pre-clone. A similar structure can be formed using the terms with respect to a variety, giving the pre-clone of a variety. The normalization of a variety is the model class of all identities s~~t of the variety for which both s and t contain at least one operation symbol. We show that identities in the pre-clone of the normalization of a variety correspond to normal hyperidentities in the normalization.

Słowa kluczowe

EN

clone identity; hyperidentity; Menger algebra; pre-clone

PL

algebra Mengera; supertożsamość

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2005
• Tom: Vol. 38, nr 4
• Strony: 799--810
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Denecke K.

• University of Potsdam, Institute of Mathematics, Am Neuen Palais, 14415 Potsdam, Germany

autor

Wismath S.

• University of Lethbridge, Mathematics Department, Lethbridge, Alberta, Canada T1K-3M4

Bibliografia

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