(Strongly) M-A-Injective(Flat) Modules
Abstract
Let M be a left R-module and A=\A\A∈A be a family of some submodules of M. It is introduced the classes of (strongly) M-A-injective and (strongly) M-A-flat modules which are denoted by (S) M-AI and (S) M-AF, respectively. It is obtained some characterizations of these classes and the relationships between these classes. Moreover it is investigated (S) M-AI and (S) M-AF precovers and preenvelopes of modules. It is also studied A-coherent, FA and PA modules. Finally more generally we give the characterization of S-AI(F) modules where A=\A\A∈A is a family of some left R-modules.
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.