Strongly Indecomposable Localizations of the Ring of Algebraic Integers

Abstract

As it is known, the study of ℰ-closed torsion-free abelian groups of finite rank is reduced to the description of strongly indecomposable localizations of rings of algebraic integers. In this paper, we give some conditions for strong indecomposability in terms of the algebraic number theory and consider some related questions.

Key Words:

• E-Rings
• Extreme ideal
• ℰ-Closed abelian group
• k-Indecomposability
• Localization
• Strongly indecomposable abelian group

Notes

Communicated by V. A. Artamonov.