不可分解的生物以较小的长度生存
Indecomposables live in all smaller lengths
摘要：
设$Λ$是有限维$k$ -代数，且$k$是代数闭的. Bongartz最近证明了一个长度为$n > 1$的不可分解$Λ$ -模的存在意味着长度为$n-1$的不可分解$Λ$ -模也存在。对他的论证稍加修改，我们加强了这个断言如下：如果有一个长度为$n$的不可分解模，那么也有一个可访问的模。这里，可访问模块被归纳地定义如下：首先，简单模块是可访问的。第二，一个长度为$n \ge 2$的模是可访问的，只要它是不可分解的，并且有一个长度为$n-1$的子模或因子模是可访问的。
英文摘要：
Let $Λ$ be a finite-dimensional $k$-algebra with $k$ algebraically closed. Bongartz has recently shown that the existence of an indecomposable $Λ$-module of length $n > 1$ implies that also indecomposable $Λ$-modules of length $n-1$ exist. Using a slight modification of his arguments, we strengthen the assertion as follows: If there is an indecomposable module of length $n$, then there is also an accessible one. Here, the accessible modules are defined inductively, as follows: First, the simple modules are accessible. Second, a module of length $n \ge 2$ is accessible provided it is indecomposable and there is a submodule or a factor module of length $n-1$ which is accessible.
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。
