Pure-injective hulls of modules over valuation rings

Details Pure-injective hulls of modules over valuation rings Pure-injective hulls of modules over valuation rings

2004-11-22

arxiv.org/abs/math/0411482v2

Journal of Pure and Applied Algebra 207 (2006) 63--76

Mathematics

Rings and Algebras

Scientific paper

10.1016/j.jpaa.2005.09.002

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.

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