Prime Submodules and a Sheaf on the Prime Spectra of Modules

Abstract

We define and investigate a sheaf of modules on the prime spectra of modules, and it is shown that there is an isomorphism between the sections of this sheaf and the ideal transform module.

Key Words:

• Ideal transform modules
• Local cohomology modules
• Prime submodules
• Sheaf of modules
• Zariski topology

2010 Mathematics Subject Classification:

• Primary 13C13
• Secondary 13C99, 13D45, 14A25, 14A99

ACKNOWLEDGMENT

The authors specially thank the referee for the helpful suggestions and comments.

Dedicated to Professor Rahim Zaare Nahandi (University of Tehran).

Notes

Communicated by I. Swanson.