Smith, P.F. and Woodward, A.R. (2007) Krull dimension of bimodules. Journal of Algebra, 310(1), pp. 405-412. (doi: 10.1016/j.jalgebra.2007.01.013)
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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.
| Item Type: | Articles |
|---|---|
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Smith, Professor Patrick |
| Authors: | Smith, P.F., and Woodward, A.R. |
| Subjects: | Q Science > QA Mathematics |
| College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
| Journal Name: | Journal of Algebra |
| ISSN: | 0021-8693 |
| ISSN (Online): | 1090-266X |
| Published Online: | 19 January 2007 |
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