The partial clone of linear terms
- Generalizing a linear expression over a vector space, we call a term of an arbitrary type tau 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 tau, 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.
| Author details: | Klaus-Dieter DeneckeORCiDGND |
|---|---|
| DOI: | https://doi.org/10.1134/S0037446616040030 |
| ISSN: | 0037-4466 |
| ISSN: | 1573-9260 |
| Title of parent work (English): | Siberian Mathematical Journal |
| Publisher: | Pleiades Publ. |
| Place of publishing: | New York |
| Publication type: | Article |
| Language: | English |
| Year of first publication: | 2016 |
| Publication year: | 2016 |
| Release date: | 2020/03/22 |
| Tag: | clone; linear hyperidentity; linear hypersubstitution; linear identity; linear term; partial clone |
| Volume: | 57 |
| Number of pages: | 10 |
| First page: | 589 |
| Last Page: | 598 |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| Peer review: | Referiert |
