论文标题
直接产品的多核类似物
Polyadic analogs of direct product
论文作者
论文摘要
We propose a generalization of the external direct product concept to polyadic algebraic structures which introduces novel properties in two ways: the arity of the product can differ from that of the constituents, and the elements from different multipliers can be \textquotedblleft entangled\textquotedblright\ such that the product is no longer componentwise.我们要保留的主要属性是关联性，它是通过使用前面提供的关联Quiver技术来获得的。对于多层半群和组，我们介绍了两个外部产品：1）迭代的直接产品，它是构成的，但可能与乘数不同； 2）异性产品（功率）是非局限性的，并通过与前面介绍的异态概念的类比构建。在哪些情况下，多核基团的乘积本身可以是多层群体。以同样的方式，多核环和磁场的外部产物也被普遍化。最外来的情况是当所有乘数都是ZeroLess字段时，可以是多核场的外部产物（与二进制场相反）。提出了许多说明性的具体示例。
We propose a generalization of the external direct product concept to polyadic algebraic structures which introduces novel properties in two ways: the arity of the product can differ from that of the constituents, and the elements from different multipliers can be \textquotedblleft entangled\textquotedblright\ such that the product is no longer componentwise. The main property which we want to preserve is associativity, which is gained by using the associativity quiver technique provided earlier. For polyadic semigroups and groups we introduce two external products: 1) the iterated direct product which is componentwise, but can have arity different from the multipliers; 2) the hetero product (power) which is noncomponentwise and constructed by analogy with the heteromorphism concept introduced earlier. It is shown in which cases the product of polyadic groups can itself be a polyadic group. In the same way the external product of polyadic rings and fields is generalized. The most exotic case is the external product of polyadic fields, which can be a polyadic field (as opposed to the binary fields), when all multipliers are zeroless fields. Many illustrative concrete examples are presented.
