A Note on Comultiplication Modules

• 作者: YongduoWang Yang Liu
• 来源期刊: 代数集刊:英文版
• 学科: 数学
• 关键词: 子模块 乘法 注记 热电联产 DAC 交换环 任意子 模M
• 年，卷（期）: 2014,（1）
• 页码范围: 147-150
• 页数: 4页
• 分类号: O121.5
• 语种: 中文

摘要

Let R be a commutative ring with identity. An R-module M is said to be a comultiplication module if for every submodule N of M, there exists an ideal I of R such that N = (0:M I). In this paper, we show: (1) If M is a comultiplication module and N is a copure submodule of M, then M/N is a comultiplication module. (2) If M is a comultiplication module satisfying the DAC and N ≤ M, then N ≤eM if and only if there exists I ≤ R such that N = (0 :M I). (3) If M is a comultiplication module satisfying the DAC, then M is finitely cogenerated. Finally, we give a partial answer to a question posed by Ansari-Toroghy and Farshadifar.