ADS modules

作者：Alahmadi Adel; Jain S K; Leroy Andre^*

来源：Journal of Algebra, 2012, 352(1): 215-222.

DOI：10.1016/j.jalgebra.2011.10.035

• Modules
• Direct sums
• ADS modules
• Injective modules
• Quasi-continuous modules

We study the class of ADS rings and modules introduced by Fuchs (1970) [F]. We give some connections between this notion and classical notions such as injectivity and quasi-continuity. A simple ring R such that R-R is ADS must be either right self-injective or indecomposable as a right R-module. Under certain conditions we can construct a unique ADS hull up to isomorphism. We introduce the concept of completely ADS modules and characterize completely ADS semiperfect right modules as direct sum of semisimple and local modules.

• 出版日期2012-2-15