Weak-Injective Modules

ABSTRACT

Pure-injective and RD-injective R-modules over domains R have been investigated by many authors. We introduce another class of R-modules, called weak-injective modules, which turn out to be useful in addressing several unanswered questions between the two classes of modules. We also find that this class is an envelope class over any domain, giving a partial answer to the existence of envelope classes in the hierarchy of injective and divisible modules.

Communicated by I. Swanson.

Keywords:

• Cover and envelope class
• Flat, Projective and weak dimension
• Prüfer domains
• Pure-injective
• RD-injective, and weak-injective modules
• Torsion-free modules and modules of weak dimension ≤1

Mathematics Subject Classification:

• 13C11
• 13G05

ACKNOWLEDGMENTS

The article was completed while the author was visiting Tulane University. He expresses his thanks to the Department of Mathematics of Tulane University for the hospitality, and to Professor Laszlo Fuchs for several discussions on the subject. He also thanks the referee for valuable comments.