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One-directed indecomposable pure injective modules over string algebras. (English) Zbl 1085.16011
This work is a further step in Ringel’s program classifying indecomposable pure injective modules over finite-dimensional string algebras. As the main result, the authors prove in Theorem 5.4 that the isomorphism type of an indecomposable pure injective module \(M\) over a string algebra admitting a one-sided word \(w(m)\) for some nonzero element \(m\in M\) is determined by \(w(m)\) and, conversely, for every one-sided word \(w\) there exists an indecomposable pure injective module \(M\) with \(w=w(m)\) for some \(0\neq m\in M\). Moreover, this correspondence is one-to-one for infinite words. Several interesting applications of this result are given.

MSC:
16G20 Representations of quivers and partially ordered sets
16D50 Injective modules, self-injective associative rings
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