On Matlis dualizing modules

Edgar E. Enochs, J. A. López-Ramos, B. Torrecillas
2002 International Journal of Mathematics and Mathematical Sciences  
We consider rings admitting a Matlis dualizing moduleE. We argue that ifRadmits 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.
doi:10.1155/s0161171202109203 fatcat:c6fv6vecn5awvabafk7ubyiuly