论文标题
在某些非传统弦乐代数的稳定激进
On the stable radical of some non-domestic string algebras
论文作者
论文摘要
我们在字符串代数$λ$中介绍了质子乐队的概念，并将其与$λ$相关联桥梁颤抖。然后，我们引入了一种“递归系统”的新技术，以表明有限尺寸字符串模块之间的图映射位于其稳定的激素中。此外，我们根据其桥箭量的某些连接性特性研究了两类非传统的弦乐代数。 `元 - $ \ bigCup $ -Cyclic'String代数构成了第一类，其本质上的特征是每个有限字符串都是频段的子字符串。扩展此类我们具有“无元信号”字符串代数，其特征是字符串模块之间的图形级别的二分法陈述 - 类似的映射要么具有有限的等级，要么是稳定的自由基。他们的稳定等级只能从$ \ {ω，ω+1，ω+2 \} $中获取值。
We introduce the concept of a prime band in a string algebra $Λ$ and use it to associate to $Λ$ its finite bridge quiver. Then we introduce a new technique of `recursive systems' for showing that a graph map between finite dimensional string modules lies in its stable radical. Further we study two classes of non-domestic string algebras in terms of some connectedness properties of its bridge quiver. `Meta-$\bigcup$-cyclic' string algebras constitute the first class that is essentially characterized by the statement that each finite string is a substring of a band. Extending this class we have `meta-torsion-free' string algebras that are characterized by a dichotomy statement for ranks of graph maps between string modules--such maps either have finite rank or are in the stable radical. Their stable ranks can only take values from $\{ω,ω+1,ω+2\}$.
