论文标题
代数结构的多层化
Polyadization of algebraic structures
论文作者
论文摘要
提出了多核代数结构的半透明性概念的概括。如果可以以块对角矩阵形式（导致Wedderburn的分解）表示半神经结构，则通过嵌段型矩阵给出了多层结构的一般形式。我们将这些形式结合在一起，以获得半神经非衍生多层结构（两种“双重”分解）的一般形状。然后，我们介绍了多层化概念（“多核构造者”），根据该概念，可以从给定的二进制结构中构造任何ARITY的非衍生多核代数结构。还讨论了超对称结构的多层化。通过对二进制结构的直接功率进行操作的“变形”被定义并用于获得非衍生的多层乘法。给出了新结构的说明性具体示例。
A generalization of the semisimplicity concept for polyadic algebraic structures is proposed. If semisimple structures can be presented in block diagonal matrix form (resulting in the Wedderburn decomposition), a general form of polyadic structures is given by block-shift matrices. We combine these forms to get a general shape of semisimple nonderived polyadic structures ("double" decomposition of two kinds). We then introduce the polyadization concept (a "polyadic constructor") according to which one can construct a nonderived polyadic algebraic structure of any arity from a given binary structure. The polyadization of supersymmetric structures is also discussed. The "deformation" by shifts of operations on the direct power of binary structures is defined and used to obtain a nonderived polyadic multiplication. Illustrative concrete examples for the new constructions are given.
