Weak-Injective Modules of Weak Dimension at Most One

Abstract

We consider modules over integral domains R. A main purpose is to show that certain module properties assumed on R-modules of weak dimension ≤1 imply that these properties are shared by all modules in the category of R-modules.

Also we prove several results involving modules of weak dimension ≤1.

Key Words:

• Coherent domains
• Copure-flat modules
• Flat modules
• Matlis domains
• Matlis-
• Enochs-
• and Warfield-cotorsion modules
• Modules of weak dimension ≤1
• Pure-injective
• Weak-injective

2000 Mathematics Subject Classification:

• Primary 13C11, 13G05
• Secondary 13C05

ACKNOWLEDGMENTS

Portions of this article were completed while the author was visiting Tulane University in New Orleans. He expresses his thanks to the Department of Mathematics of Tulane University for the hospitality. He also thanks Professor Laszlo Fuchs for valuable comments on the article.

Notes

Communicated by R. Wiegand.