论文标题
$λ$ - 单向逆的单体产品是微弱的Schreier扩展
$λ$-Semidirect Products of Inverse Monoids are Weakly Schreier Extensions
论文作者
论文摘要
用核K：n-> g，cokernel E：g-> h和分裂s：h-> g的单体分裂扩展是弱schreier。此类扩展的激励例子是拓扑空间的Artin胶合物，当然还有它们概括的单型物体的Schreier扩展。在本文中，我们表明，逆肌反向的lambda-离子产物也是弱施雷尔扩展的示例。弱Schreier扩展的表征揭示了Lambda-偏离产物的结构。两种单型物体之间的一组弱的Schreier扩展配备有天然的Poset结构，该结构在两个反向单体之间引起了lambda-偏离的乘积的顺序。我们表明，Artin Glueings实际上是Lambda-semidirect产品，并以此为灵感来识别一类类似Artin的Lambda-semidirect产品。我们表明，在上述顺序中，与这种特殊类别的lambda-偏离产品相连。
A split extension of monoids with kernel k: N -> G, cokernel e: G -> H and splitting s: H -> G is weakly Schreier if each element g in G can be written g = k(n)se(g) for some n in N. The characterization of weakly Schreier extensions allows them to be viewed as something akin to a weak semidirect product. The motivating examples of such extensions are the Artin glueings of topological spaces and, of course, the Schreier extensions of monoids which they generalise. In this paper we show that the lambda-semidirect products of inverse monoids are also examples of weakly Schreier extensions. The characterization of weakly Schreier extensions sheds some light on the structure of lambda-semidirect products. The set of weakly Schreier extensions between two monoids comes equipped with a natural poset structure, which induces an order on the set of lambda-semidirect products between two inverse monoids. We show that Artin glueings are in fact lambda-semidirect products and inspired by this identify a class of Artin-like lambda-semidirect products. We show that joins exist for this special class of lambda-semidirect product in the aforementioned order.
