The partial clone of linear terms
- Authors: Denecke K.1,2
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Affiliations:
- Institute of Mathematics
- Department of Mathematics
- Issue: Vol 57, No 4 (2016)
- Pages: 589-598
- Section: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/170580
- DOI: https://doi.org/10.1134/S0037446616040030
- ID: 170580
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Abstract
Generalizing a linear expression over a vector space, we call a term of an arbitrary type τ linear if its every variable occurs only once. Instead of the usual superposition of terms and of the total many-sorted clone of all terms in the case of linear terms, we define the partial many-sorted superposition operation and the partial many-sorted clone that satisfies the superassociative law as weak identity. The extensions of linear hypersubstitutions are weak endomorphisms of this partial clone. For a variety V of one-sorted total algebras of type τ, we define the partial many-sorted linear clone of V as the partial quotient algebra of the partial many-sorted clone of all linear terms by the set of all linear identities of V. We prove then that weak identities of this clone correspond to linear hyperidentities of V.
About the authors
K. Denecke
Institute of Mathematics; Department of Mathematics
Author for correspondence.
Email: klausdenecke@hotmail.com
Germany, Potsdam; KhonKaen