论文标题
一般代数的较弱的Schreier扩展
Weakly Schreier extensions for general algebras
论文作者
论文摘要
Schreier分裂扩展是一项相当大但又被理解的单型扩展类别，它概括了群体分裂扩展的某些方面。此简短说明提供了一种在一般代数结构中定义和研究类似类别的分割扩展的方法（由$θ$进行参数）。这些概括了弱的schreier扩展，以及半阿伯式品种的一般扩展（使用其句法表征中出现的$θ$）。 $θ$的不同选择再次限制在单型剂的情况下，导致了一类新的单体扩展，比弱的Schreier拆分扩展更一般。
Weakly Schreier split extensions are a reasonably large, yet well-understood class of monoid extensions, which generalise some aspects of split extensions of groups. This short note provides a way to define and study similar classes of split extensions in general algebraic structures (parameterised by a term $θ$). These generalise weakly Schreier extensions of monoids, as well as general extensions of semi-abelian varieties (using the $θ$ appearing in their syntactical characterisation). Restricting again to the case of monoids, a different choice of $θ$ leads to a new class of monoid extensions, more general than the weakly Schreier split extensions.
