On the Prime Spectrum of a Module and Zariski Topologies

Abstract

Let R be a commutative ring with identity, and let M be an R-module. There are different Zariski topologies defined on the prime spectrum Spec(M). In this article, we will determine and compare various topological properties of these topological spaces and investigate them from the point of view of spectral space.

Key Words:

• Prime submodule
• Primeful module
• Spectral space
• Top module
• X-Injective module
• Zariski topology

2000 Mathematics Subject Classification:

• 13C13
• 13C99

ACKNOWLEDGMENT

The authors would like to thank the referee for his/her valuable comments.

Notes

Communicated by I. Swanson.