n-SUMMABLE VALUATED p(n)-SOCLES AND PRIMARY ABELIAN GROUPS

作者：Danchev Peter V; Keef Patrick W^*

来源：Communications in Algebra, 2010, 38(9): 3137-3153.

DOI：10.1080/00927870903164651

• Primary abelian group
• Summable
• Valuated group
• Valuated vector space

Generalizing the classical concept of a valuated vector space, we introduce the notion of a valuated p(n)-socle. A valuated p(n)-socle is said to be n-summable if it is isometric to the valuated direct sum of countable valuated groups. Many properties of these objects are established, and in particular, they are shown to be completely classifiable using Ulm invariants, providing a strong connection with the theory of direct sums of countable abelian p-groups. The resulting theory is then applied to the category of primary abelian groups.

• 出版日期2010