%0 Journal Article
%T Pure-injective hulls of modules over valuation rings
%A Francois Couchot
%J Mathematics
%D 2004
%I arXiv
%R 10.1016/j.jpaa.2005.09.002
%X If $\hat{R} is the pure-injective hull of a valuation ring $R$, it is proved that $\hat{R}\otimes\_RM$ is the pure-injective of $M$, for each finitely generated module $M$. Moreover, $\hat{R}\otimes\_RM\simeq\oplus\_{1\leq k\leq n}\hat{R}/A\_k\hat{R}$, where $A\_1,...,A\_n$ is the annihilator sequence of $M$. The pure-injective hulls of uniserial or polyserial modules are also investigated. Any two pure-composition series of a countably generated polyserial module are isomorphic.
%U http://arxiv.org/abs/math/0411482v2