Finitely generated torsion-free modules over integrally closed domains

摘要

Let M be a finitely generated torsion-free module over a Dedekind domain R and MX be a polynomial module over RX, where X is an indeterminate. It is shown that M and MX are both generalized Dedekind modules over R and RX, respectively. These results are obtained using a relation between the v-submodules of M (v-submodules of MX) and ideals of R (invertible ideals of RX).