On Matlis dualizing modules
We consider rings admitting a Matlis dualizing module E. We argue that if R admits two such dualizing modules, then a module is reflexive with respect to one if and only if it is reflexive with respect to the other. Using this fact we argue that the number (whether finite or infinite) of distinct d...
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Hindawi Limited
2002-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171202109203 |
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doaj-80f19d9e342b466199c4279daa20f5172020-11-24T22:27:27ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252002-01-01301165966510.1155/S0161171202109203On Matlis dualizing modulesEdgar E. Enochs0J. A. López-Ramos1B. Torrecillas2Department of Mathematics, University of Kentucky, Lexington, KY 40506, USADepartamento de Algebra y Análisis Matemático, Universidad de Almería, Almería 04120, SpainDepartamento de Algebra y Análisis Matemático, Universidad de Almería, Almería 04120, SpainWe consider rings admitting a Matlis dualizing module E. We argue that if R admits two such dualizing modules, then a module is reflexive with respect to one if and only if it is reflexive with respect to the other. Using this fact we argue that the number (whether finite or infinite) of distinct dualizing modules equals the number of distinct invertible (R,R)-bimodules. We show by example that this number can be greater than one.http://dx.doi.org/10.1155/S0161171202109203 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Edgar E. Enochs J. A. López-Ramos B. Torrecillas |
| spellingShingle |
Edgar E. Enochs J. A. López-Ramos B. Torrecillas On Matlis dualizing modules International Journal of Mathematics and Mathematical Sciences |
| author_facet |
Edgar E. Enochs J. A. López-Ramos B. Torrecillas |
| author_sort |
Edgar E. Enochs |
| title |
On Matlis dualizing modules |
| title_short |
On Matlis dualizing modules |
| title_full |
On Matlis dualizing modules |
| title_fullStr |
On Matlis dualizing modules |
| title_full_unstemmed |
On Matlis dualizing modules |
| title_sort |
on matlis dualizing modules |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
2002-01-01 |
| description |
We consider rings admitting a Matlis dualizing module E. We argue that if R admits two such dualizing modules, then a module is reflexive with respect to one if and only if it is reflexive with respect to the other. Using this fact we argue that
the number (whether finite or infinite) of distinct dualizing modules equals the number of distinct invertible
(R,R)-bimodules. We show by example that this number can be greater than one. |
| url |
http://dx.doi.org/10.1155/S0161171202109203 |
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AT edgareenochs onmatlisdualizingmodules AT jalopezramos onmatlisdualizingmodules AT btorrecillas onmatlisdualizingmodules |
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