On Algebraically Compact Λ-Modules

Abstract

We study the structure and properties of algebraically compact modules over Λ = ℤ _p [[T]], the power series ring over the p-adic integer ring.

Key Words:

• Algebraically compact
• Pure-injectivity
• Λ-module

2000 Mathematics Subject Classification:

• 13C05
• 11R23

ACKNOWLEDGMENTS

I am most grateful to Professor Shin Nakano and Professor Yoshitaka Hachimori who gave me continuous encouragement and valuable advice. I thank Yoshichika Iizuka for various discussions on Iwasawa theory and module theory.

Notes

Communicated by K. M. Rangaswamy.