Pure-injective hulls of modules over valuation rings

Abstract

If $\hat{R}isthepure-injectivehullofavaluationring$R$,itisprovedthat$\hat{R}\otimes\_RM$isthepure-injectiveof$M$,foreachfinitelygeneratedmodule$M$.Moreover,$\hat{R}\otimes\_RM\simeq\oplus\_{1\leq k\leq n}\hat{R}/A\_k\hat{R}$,where$A\_1,...,A\_n$istheannihilatorsequenceof$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.

References in corpus (1)

• Injective modules and fp-injective modules over valuation rings