论文标题
副命令有限领域产品之间的封闭式限制功能集
Closed sets of finitary functions between products of finite fields of coprime order
论文作者
论文摘要
我们研究了有限字段$ \ prod_ {j = 1}^m \ mathbb {f} _ {q_j} = \ Mathbb {K k} $的有限产物的适用函数，以有限字段$ \ prod_ = 1}^n \ mathbb {i = 1}^n \ mathbb {f i}其中$ | \ mathbb {k} | $和$ | \ mathbb {f} | $是coprime。 $（\ mathbb {f}，\ mathbb {k}）$ - 线性封闭的克隆是这些函数的子集，这些功能是在右侧和左侧带有线性映射的构图下封闭的子集。 我们通过$ \ mathbb {f} _p [\ Mathbb {k}^{\ times}] $ - suppodules的$ \ mathbb {f} _p^} _p^{\ mathbb {k} $ mon $ \ mathbb { $ \ mathbb {k} = \ prod_ {i = 1}^m \ mathbb {f} _ {q_i} $。此外，我们证明了函数的每个子集都是由一组单一函数生成的，并且我们为不同的$（\ mathbb {f}，\ mathbb {k}）$线性封闭的clonoids提供了上限。
We investigate the finitary functions from a finite product of finite fields $\prod_{j =1}^m\mathbb{F}_{q_j} = \mathbb{K}$ to a finite product of finite fields $\prod_{i =1}^n\mathbb{F}_{p_i} = \mathbb{F}$, where $|\mathbb{K}|$ and $|\mathbb{F}|$ are coprime. An $(\mathbb{F},\mathbb{K})$-linearly closed clonoid is a subset of these functions which is closed under composition from the right and from the left with linear mappings. We give a characterization of these subsets of functions through the $\mathbb{F}_p[\mathbb{K}^{\times}]$-submodules of $\mathbb{F}_p^{\mathbb{K}}$, where $\mathbb{K}^{\times}$ is the multiplicative monoid of $\mathbb{K} = \prod_{i=1}^m\mathbb{F}_{q_i}$. Furthermore we prove that each of these subsets of functions is generated by a set of unary functions and we provide an upper bound for the number of distinct $(\mathbb{F},\mathbb{K})$-linearly closed clonoids.
