Galois theory for clones and superclones
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Nikolay A. Peryazev
und
Ivan K. Sharankhaev
Abstract
We study clones (closed sets of operations that contain projections) and superclones on finite sets. According to A. I. Mal’tsev a clone may be considered as an algebra. If we replace algebra universe with a set of multioperations and add the operation of simplest equation solvability then we will obtain an algebra called a superclone. The paper establishes Galois connection between clones and superclones.
Originally published in Diskretnaya Matematika (2015) 27, №4, 79–93 (in Russian).
Funding source: Russian Foundation for Basic Research
Award Identifier / Grant number: 12-01-000351a
Funding statement: Research was supported by RFBR, project number 12-01-000351a
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© 2016 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Research Article
- Characterization of almost perfect nonlinear functions in terms of subfunctions
- Research Article
- Estimates for distribution of the minimal distance of a random linear code
- Research Article
- The distributions of interrecord fillings
- Research Article
- Galois theory for clones and superclones
- Research Article
- Overgroups of order 2n additive regular groups of a residue ring and of a vector space
Artikel in diesem Heft
- Frontmatter
- Research Article
- Characterization of almost perfect nonlinear functions in terms of subfunctions
- Research Article
- Estimates for distribution of the minimal distance of a random linear code
- Research Article
- The distributions of interrecord fillings
- Research Article
- Galois theory for clones and superclones
- Research Article
- Overgroups of order 2n additive regular groups of a residue ring and of a vector space
