Module-Theoretic Characterizations of t-Linkative Domains

Abstract

If R is an integral domain, we extend to any R-module the notion of semi-divisorial envelope, or w-envelope, defined by Wang and McCasland for torsion-free R-modules, and introduce and study the related notions of co-semi-divisoriality and w-nullity. These concepts are then used to give new module-theoretic characterizations of t-linkative domains, a class of domains widely considered in multiplicative ideal theory.

Key Words:

• Co-semi-divisorial
• w-Isomorphic
• t-Linkative
• t-Linked
• w-Null
• (essentially) Pseudo-t-linkative
• Semi-divisorial
• Semi-divisorial envelope
• Weakly w-flat

2000 Mathematics Subject Classification:

• 13A15
• 13Bxx
• 13Cxx
• 13D07
• 13Dxx
• 13G05

ACKNOWLEDGMENTS

The author would like to thank the referee for his/her many helpful suggestions.

Notes

Communicated by A. K. Singh.