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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
##### Keywords:
pure injective modules; string algebras; infinite words
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