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Pré-Publication, Document De Travail Année : 2004

Pure-injective hulls of modules over valuation rings

Résumé

If $\widehat{R} is the pure-injective hull of a valuation ring $R$, it is proved that $\widehat{R}\otimes_RM$ is the pure-injective of $M$, for each finitely generated module $M$. Moreover, $\widehat{R}\otimes_RM\simeq\oplus_{1\leq k\leq n}\widehat{R}/A_k\widehat{R}$, where $A_1,\dots,A_n$ 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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Dates et versions

hal-00003336 , version 1 (22-11-2004)
hal-00003336 , version 2 (07-09-2006)

Identifiants

Citer

Francois Couchot. Pure-injective hulls of modules over valuation rings. 2004. ⟨hal-00003336v1⟩
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