On orthodox semigroups with $\Pi (L^1\times R^1)$-embeddable band of idempotents

手头的申请是申请人2016年6月至9月至2017年6月至9月的申请的续期。在关于这个项目的初步工作的早期状态中，我们被引导到一个扩展的概念，它是表示半群的一个重要工具。为了验证这个概念是否有助于我们的考虑，我们意外地在两个突出的代表上获得了一些统一结构的理论结果，即Birget-Rhodes[13]和Margolis-Meakin群展开[21]。因此，项目组决定首先详细阐述这些发现。与此同时，这在2010年成功地实现了。特别是，我们的结果为[21]和[26]中证明的一些众所周知的事实提供了相当简单的证明。因此，除其他事项外，申请项目的延续以解决推迟的原始任务似乎是合理的。

The application at hand is a renewal of the applicant's one from June to September 2016 to June to September 2017. In an early state of preliminary work concerning this project we were led to the notion of an expansion which is an important tool for the representation of semigroups in general. Checking out whether this concept could be helpful for our considerations, we unexpectedly obtained some unifying structure theoretical results on two prominent representatives, namely the Birget-Rhodes [13] and the Margolis-Meakin group expansion [21]. Thus the project group decided to elaborate these findings first. This has meanwhile successfully been done in [9]. In particular our results provide considerably simpler proofs of some well known facts proven in [21] and [26]. Hence it seems to be reasonable to apply for a continuation of the project to tackle, among other things, the postponed original task.