Self-pure-generators over Dedekind domains

JOURNAL OF PURE AND APPLIED ALGEBRA

卷:223

Article

Breaz, Simion¹ 

[1] Babes Bolyai Univ, Fac Math & Comp Sci, Str Mihail Kogalniceanu 1, Cluj Napoca 400084, Romania

关键词: Dedekind domain;    Finite rank torsion-free module;    Pure submodule;    Self-pure-generator;    Type;   

DOI  :  10.1016/j.jpaa.2019.03.016

来源: Elsevier

【 摘 要 】

We prove that all pure submodules of a finite rank torsion-free module A over a Dedekind domain are A-generated (i.e. A is a self-pure-generator) if and only if A has a rank 1 direct summand B such that type(B) is the inner type of A. This result is applied to describe the direct products of torsion-free groups of finite rank which are self-pure-generators. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free