On Modules Whose Singular Subgenerated Modules Are Weakly Injective

• 来源期刊: 代数集刊（英文版）
• 学科: 数学
• 关键词: weakly injective modules singular modules SI-rings SI-modules
• 年，卷（期）: 2001,（2）
• 页码范围: 227-236
• 页数: 10页
• 分类号: O1
• 语种: 英文

摘要

Rings over which every singular right module is injective (briefly,right SI-rings) were introduced and investigated by Goodearl. Weakly injective modules, as a generalization of injective modules, were introduced by Jain and modules are weakly injective, which we call SwI-rings. This concept is extended to SwI-modules, i.e., modules whose singular subgenerated modules are weakly injective. Several characterizations and properties of SwI-rings and SwI-modules are obtained which generalize some earlier known results on SI-rings and weakly semisimple rings.