International Journal of Mathematics and Mathematical Sciences
Volume 30 (2002), Issue 11, Pages 659-665
doi:10.1155/S0161171202109203
On Matlis dualizing modules
Edgar E. Enochs1
, J.A. López-Ramos2
and B. Torrecillas2
1Department of Mathematics, University of Kentucky, Lexington 40506, KY, USA
2Departamento de Algebra y Análisis Matemático, Universidad de Almería, Almería 04120, Spain
Abstract
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.