论文标题
半同态的逆向也是半同态的
Half-isomorphisms whose inverses are also half-isomorphisms
论文作者
论文摘要
令$（g，*）$和$（g'，\ cdot）$为groupoids。如果$ f（x*y）\ in \ {f（x）\ cdot f（y），f（y）\ cdot f（x）\ cdot f（x）\ in \ f（x）\ cdot f（x）\ in b bioject $ f：g \ rightArrow g'$，则称为半同态。群体素对自身的半态性是半自形的。如果$ f^{ - 1} $也是半同态，则为半同态$ f $被称为特殊。在本文中，获得了对群体和准群的特殊半晶状体存在的必要条件。此外，还提供了一些非特殊半自动性的例子，以实现无限顺序的循环。
Let $(G,*)$ and $(G',\cdot)$ be groupoids. A bijection $f: G \rightarrow G'$ is called a half-isomorphism if $f(x*y)\in\{f(x)\cdot f(y),f(y)\cdot f(x)\}$, for any $ x, y \in G$. A half-isomorphism of a groupoid onto itself is a half-automorphism. A half-isomorphism $f$ is called special if $f^{-1}$ is also a half-isomorphism. In this paper, necessary and sufficient conditions for the existence of special half-isomorphisms on groupoids and quasigroups are obtained. Furthermore, some examples of non-special half-automorphisms for loops of infinite order are provided.
