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 the 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}.

我们在字符串代数Λ中引入素数带的概念，并将其与Λ的有限桥颤动相关联。然后，我们介绍了一种“递归系统”的新技术，以显示有限维字符串模块之间的图映射位于稳定根中。进一步，根据其桥颤动的一些连通性，我们研究了两类非家庭弦代数。'Meta- \（\\ bigcup \）“循环”字符串代数构成了第一类，其基本特征是每个有限字符串是一个带的子字符串。扩展此类后，我们有了“无元扭曲”字符串代数，这些代数的特征是对字符串模块之间的图形映射的等级进行二分法声明-这样的映射要么具有有限的等级，要么处于稳定的根中。它们的稳定等级只能采用{ ω，ω + 1，ω + 2}中的值。