论文标题
单体扩展的商及其与Baer总和的相互作用
Quotients of monoid extensions and their interplay with Baer sums
论文作者
论文摘要
单体的固定延伸概括了组的扩展，特殊的schreier扩展和leech通过单体对组的正常扩展。他们与组扩展名共享许多属性，包括当内核是Abelian时的Baer总和概念。但是，与群体扩展（带有固定的核和凝糖岩）不同，它们之间可能存在非平凡的态度。我们探讨了固定扩展类别的结构，并将其与第二个共同体学组的类似物相关联。最后，将顺序结构和添加剂结构组合在一起，从而提供了索引的扩展逆半数群。这些反过来可以将它们合并为反类别。
Cosetal extensions of monoids generalise extensions of groups, special Schreier extensions of monoids and Leech's normal extensions of groups by monoids. They share a number of properties with group extensions, including a notion of Baer sum when the kernel is abelian. However, unlike group extensions (with fixed kernel and cokernel) there may be nontrivial morphisms between them. We explore the structure of the category of cosetal extensions and relate it to an analogue of second cohomology groups. Finally, the order structure and additive structures are combined to give an indexed family of inverse semigroups of extensions. These in turn can be combined into an inverse category.
