拟群自同态的Bruck分解
Bruck decomposition for endomorphisms of quasigroups
摘要：
1944年，R。H.布鲁克描述了一个非常普遍的建设方法，他所谓的扩展一套准群。我们用它来构造LF-拟群的一类例子，其中映射$e(x)=x\backslash x$的像是一个群。更一般地说，我们考虑各种拟群的性质所定义的地图$e$是一个自同态和其子品种的形象的地图$e$是一个群体。我们的特点拟群属于这些品种使用他们的Bruck分解相对于地图$e$。
英文摘要：
In the year 1944 R. H. Bruck has described a very general construction method which he called the extension of a set by a quasigroup. We use it to construct a class of examples for LF-quasigroups in which the image of the map $e(x)=x\backslash x$ is a group. More generally, we consider the variety of quasigroups which is defined by the property that the map $e$ is an endomorphism and its subvariety where the image of the map $e$ is a group. We characterize quasigroups belonging to these varieties using their Bruck decomposition with respect to the map $e$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
