论文标题
包含$ \ mathbb {z} _ {pq} $ mal'cev操作的克隆
Clones containing the Mal'cev operation of $\mathbb{Z}_{pq}$
论文作者
论文摘要
我们从$ \ mathbb {z} _ {pq} $到$ \ mathbb {z} _ {pq} $从$ \ mathbb {z} _ {pq} $调查了finality函数。我们证明了集合$ \ mathbb {z} _ {pq} $的所有克隆的晶格，其中包含$ \ mathbb {z} _ {pq} $的添加是有限的。我们通过注入函数通过注入函数为所有$（\ Mathbb {z} _p，\ Mathbb {Z} _Q）$线性封闭的clonoids to $ p+1 $ power和所有的晶格的晶格提供了该晶格的基数的上限。 $（\ Mathbb {z} _Q，\ Mathbb {z} _p）$ - $ q+1 $ power线性封闭的clonoids。这些晶格在Arxiv：1910.11759中进行了研究，在那里我们可以找到它们的确切基数。此外，我们证明这些克隆可以通过最多$ max（\ {p，q \}）$的一组Arity函数生成。
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 $(\mathbb{Z}_q,\mathbb{Z}_p)$-linearly closed clonoids to the $q+1$ power. These lattices are studied in arXiv:1910.11759 and there we can find the exact cardinality of them. Furthermore, we prove that these clones can be generated by a set of functions of arity at most $max(\{p,q\})$.
