左半近环、群半直积与左可消左半brace
Left seminear-rings, groups semidirect products and left cancellative left semi-braces
AI总结：
本文建立左半brace与左半近环、群半直积之间的对应，并据此分类规模为$pq$和$2p^2$的特定左可消左半brace，同时分析其多种幂零性。
摘要：
我们研究左可消左半brace与其他已有代数结构之间的若干关系。特别地，我们证明每个左半brace都可由一个左半近环产生，从而推广了文献\cite{rump2019set}中Rump给出的斜左brace与左近环之间的对应关系。此外，我们证明了某些群半直积与在幂等元集合上满足附加假设的左可消左半brace之间存在对应关系。作为应用，我们对大小为$pq$和$2p^2$、且幂等元集合$E$是乘法群的一个Sylow子群的左可消左半brace进行了分类。最后，我们研究了这些左半brace的文献\cite{catino2022nilpotency}中最近引入的各种类型的幂零性。
英文摘要：
We study some relations between left cancellative left semi-braces and other existing algebraic structures. In particular, we show that every left semi-brace arises from a left seminear-ring, extending the correspondence given by Rump between skew left braces and left near-rings in \cite{rump2019set}. Moreover, we show a correspondence between certain groups semidirect products and left cancellative left semi-braces satisfying an additional hypothesis on the set of idempotents. As an application, we classify left cancellative left semi-braces of size $pq$ and $2p^2$ such that the set of idempotents $E$ is a Sylow subgroup of the multiplicative group. Finally, we study various type of nilpotency, recently introduced in \cite{catino2022nilpotency}, of these left semi-braces.
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。
