Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4588803 | Journal of Algebra | 2007 | 8 Pages |
Abstract
Let R and S be rings and let M be a left S-, right R-bimodule such that M has Krull dimension both as a left S-module and as a right R-module and M/N has the same Krull dimension as a left S- and as a right R-module for every sub-bimodule N of M. Suppose that M is a finitely generated left S-module. Then it is proved that the Krull dimension of the right R-module M is the Krull dimension of a k-critical right R-module M/K for some prime submodule K of the right R-module M.
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