On λ-Finitely Embedded Modules

• 来源期刊: 代数集刊（英文版）
• 关键词: λ-finitely embedded λ-finite intersection property α-critical socle critical socle
• 年，卷（期）: 2005,（2）
• 页码范围: 281-292
• 页数: 12页
• 语种: 英文

摘要

In this article, we introduce and study the notion of λ-finitely embedded modules (a O-finitely embedded module is just a finitely embedded module). We extend some of the basic results of f.e. modules to λ-f.e. modules. We use this concept to give a new proof of a known result which essentially says that a module M has Krull dimension α if and only if each factor module of M is λ-f.e. for some λ≤α and α is the least ordinal with this property. It is observed that a semiprime ring R has Krull dimension λ if and only if R is λ-f.e. We improve the theorem of Matlis-Papp and some of its consequences.Finally, some known results in the literature are restated in terms of the above notion.