Clones containing the Mal'cev operation of $\mathbb{Z}_{pq}$
@article{Fioravanti2020ClonesCT, title={Clones containing the Mal'cev operation of \$\mathbb\{Z\}\_\{pq\}\$}, author={Stefano Fioravanti}, journal={arXiv: Rings and Algebras}, year={2020} }
We investigate finitary functions from $\mathbb{Z}_{pq}$ to $\mathbb{Z}_{pq}$ for two distinct prime numbers $p$ and $q$. We show that the lattice of all clones on the set $\mathbb{Z}_{pq}$ which contain the addition of $\mathbb{Z}_{pq}$ is finite. We provide an upper bound for the cardinality of this lattice through an injective function to the direct product of the lattice of all $(\mathbb{Z}_p,\mathbb{Z}_q)$-linearly closed clonoids to the $p+1$ power and the lattice of all $(\mathbb{Z}_q…
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References
SHOWING 1-10 OF 19 REFERENCES
Closed Function Sets on Groups of Prime Order
- MathematicsJ. Multiple Valued Log. Soft Comput.
- 2019
There are infinitely many non finitely generated clones above $\operatorname{Clo}({\mathbb{ Z}_p \times \mathbb(Z)_p, +})$ for $p > 2$.
Closed sets of finitary functions between finite fields of coprime order
- MathematicsAlgebra universalis
- 2020
<jats:p>We investigate the finitary functions from a finite field<jats:inline-formula><jats:alternatives><jats:tex-math>$$\mathbb {F}_q$$</jats:tex-math><mml:math…
Independence of algebras with edge term
- MathematicsInt. J. Algebra Comput.
- 2015
It is shown that the independence of finitely generated varieties with edge term can be decided by a polynomial time algorithm.
Polynomial Clones on Squarefree Groups
- MathematicsInt. J. Algebra Comput.
- 2008
It is proved that, on a set of size n, the number of clones that contain a group operation and all constant functions is finite if n is squarefree, and refutes a second conjecture from [5].
The two-valued iterative systems of mathematical logic
- Chemistry
- 1942
*Frontmatter, pg. i*CONTENTS, pg. vi*INTRODUCTION, pg. 1*Part I. PRELIMINARIES, pg. 10*PART II. DERIVATION OP CLOSED SYSTEMS, pg. 43*PART III. CO-ORDINATION AND APPLICATION, pg. 96*BIBLIOGRAPHY, pg.…
The complexity of constraint satisfaction : an algebraic approach.
- Computer Science
- 2005
An algebraic approach has proved to be very successful in studying the complexity of constraint problems and can be represented as constraint satisfaction and optimization problems.
Clones containing Mal'tsev Operations
- MathematicsInt. J. Algebra Comput.
- 1999
It is shown that the number of clones on a k element set that contain a Mal'tsev operation and all k constants is finite iff k≤3. This answers a part of a question of Ralph McKenzie and Ivo Rosenberg…
Commutative Algebra I
- Mathematics
- 2012
1 A compilation of two sets of notes at the University of Kansas; one in the Spring of 2002 by ?? and the other in the Spring of 2007 by Branden Stone. These notes have been typed