论文标题
二进制系统半群中的群体素化因素
Groupoid Factorizations in the Semigroup of Binary Systems
论文作者
论文摘要
令$（x，\ bullet）$为groupoid（二进制代数）和$ bin（x \ dot {）} $表示所有在$ x $上定义的groupoids的集合。我们在Semigroup $ \ left（bin \ left（x \ right），\ diamond \ right）$中，在二进制组乘积\ tockquotedblleft $ \ diamond $ \ diamond $ \ diamond $ \ diamond $ \ diamond $ \ diamond $ \ diamond $ \ diamond $ \ diamond $ \ diamond $ \ textquotedblright \下介绍了两种分解方法。我们得出的结论是，可以将强的非数字类固醇表示为其\ textit {％samely-}和\ textit {signature-}衍生因子的产物。此外，我们表明具有方向属性的群体是其\ textit {orient-}和\ textit {skew-}因素的产物。这些独特的因素化对于其他研究领域的各种应用可能很有用。在本文中广泛介绍到代数的申请，例如$ b/bch/bci/bci/bh/bh/bh/bi/d $ - 代数。
Let $(X,\bullet )$ be a groupoid (binary algebra) and $Bin(X\dot{)}$ denote the collection of all groupoids defined on $X$. We introduce two methods of factorization for this binary system under the binary groupoid product \textquotedblleft $\diamond $\textquotedblright\ in the semigroup $\left( Bin\left( X\right) ,\diamond \right) $. We conclude that a strong non-idempotent groupoid can be represented as a product of its \textit{% similar-} and \textit{signature-} derived factors. Moreover, we show that a groupoid with the orientation property is a product of its \textit{orient-} and \textit{skew-} factors. These unique factorizations can be useful for various applications in other areas of study. Application to algebras such as $B/BCH/BCI/BCK/BH/BI/d$-algebra are widely given throughout this paper.
