论文标题
Baer总计一类天然的单体扩展
Baer sums for a natural class of monoid extensions
论文作者
论文摘要
众所周知，具有Abelian内核组群体扩展的同构类别的特征是第二群体学组。在本文中，我们将这种扩展的特征推广到一类天然的单体扩展，即固定扩展。扩展k：n-> g，e：g-> h，其中k是包含的，e是商，如果对于所有g，g'in g in e（g）= e（g'），则在n中存在a（不一定是唯一的）n，因此g = k（n）g'。这些扩展概括了特殊的Schreier扩展名的概念，这些扩展本身就是Schreier扩展的示例。就像在分组的情况下，半程产品可以与Abelian内核相关联，我们表明，对于每个固定扩展（与Abelian群）内核一样，我们可以独特地将弱的Schreier拆分扩展相关联。弱Schreier拆分扩展的表征与一个合适的因素概念相结合，该因素设置，以提供同时赋予固定扩展的完整表征以及提供BAER总和。
It is well known that the set of isomorphism classes of extensions of groups with abelian kernel is characterized by the second cohomology group. In this paper we generalise this characterization of extensions to a natural class of extensions of monoids, the cosetal extensions. An extension k: N -> G, e: G -> H, where k is the inclusion and e is the quotient , is cosetal if for all g,g' in G in which e(g) = e(g'), there exists a (not necessarily unique) n in N such that g = k(n)g'. These extensions generalise the notion of special Schreier extensions, which are themselves examples of Schreier extensions. Just as in the group case where a semidirect product could be associated to each extension with abelian kernel, we show that to each cosetal extension (with abelian group) kernel, we can uniquely associate a weakly Schreier split extension. The characterization of weakly Schreier split extensions is combined with a suitable notion of a factor set to provide a cohomology group granting a full characterization of cosetal extensions, as well as supplying a Baer sum.
