Characterisation of PF rings by the Finite Topology on duals of R-Modules

Details Characterisation of PF rings by the Finite Topology on duals of R-Modules Characterisation of PF rings by the Finite Topology on duals of R-Modules

2011-09-14

arxiv.org/abs/1109.3003v1

An. Univ. Bucuresti Mat. Anul LII, Nr. 2(2003), pp. 189--200

Mathematics

Rings and Algebras

Original article (contains + 2 applications) published An. Univ. Bucuresti Mat. Anul LII, Nr. 2(2003), pp. 189--200. http://

Scientific paper

In this paper we study the properties of the finite topology on the dual of a module over an arbitrary ring. We aim to give conditions when certain properties of the field case are can be still found here. Investigating the correspondence between the closed submodules of the dual $M^{*}$ of a module $M$ and the submodules of $M$, we prove some characterisations of PF rings: the up stated correspondence is an anti isomorphism of lattices iff $R$ is a PF ring.

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