论文标题
Abelian无方形组的扩展
Expansions of abelian squarefree groups
论文作者
论文摘要
我们从$ \ Mathbb {z} _ {n} $到$ \ Mathbb {z} _ {n} $从$ \ mathbb {z} _ {n} $调查了finality函数。我们表明，SquareFree Set上的所有克隆的晶格$ \ Mathbb {Z} _ {P_1 \ CDOTS P_M} $包含$ \ Mathbb {Z} _ {p_1 \ cdots p_m} $的添加是有限的。我们通过注入函数为该晶格的基数提供了上限，以与所有$（\ Mathbb {z} _ {p_i}，\ Mathbb {f} _i）$ - 线性封闭的clonoids，$ Mathcal {p_i}（p _ Mathcal {p_i} {p_i} {p_i} {p_i} {p_i} {p_i} {p_i}（p_i} { \ Mathbb {f} _i）$，to $ p_i+1 $ power，其中$ \ mathbb {f} _i = \ prod_ {j \ in \ in \ {1，\ dots，m \}这些晶格在垃圾中进行了研究，我们可以找到它们的基数的上限。此外，我们证明这些克隆可以通过最多$ \ max（p_1，\ dots，p_m）$的一组Arity的功能生成。
We investigate finitary functions from $\mathbb{Z}_{n}$ to $\mathbb{Z}_{n}$ for a squarefree number $n$. We show that the lattice of all clones on the squarefree set $\mathbb{Z}_{p_1\cdots p_m}$ which contain the addition of $\mathbb{Z}_{p_1\cdots p_m}$ is finite. We provide an upper bound for the cardinality of this lattice through an injective function to the direct product of the lattices of all $(\mathbb{Z}_{p_i}, \mathbb{F}_i)$-linearly closed clonoids, $\mathcal{L}(\mathbb{Z}_{p_i}, \mathbb{F}_i)$, to the $p_i+1$ power, where $\mathbb{F}_i = \prod_{j \in \{1,\dots,m\}\backslash \{i\}}\mathbb{Z}_{p_j}$. These lattices are studied in the litterature and we can find an upper bound for cardinality of them. Furthermore, we prove that these clones can be generated by a set of functions of arity at most $\max(p_1,\dots,p_m)$.
