2018/08/02 by Mohanad Farhan Hamid, Hamid, Mohanad Farhan
Mathematics · #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #Rings, Modules, and Algebras #math.RA
paper · pdf · doi:10.48550/arxiv.1808.00883
6 pages
arxiv created 2018/08/02 · arxiv updated 2018/08/03
For a given class of R-modules Q, a module M is called Q-copure Baer injective if any map from a Q-copure left ideal of R into M can be extended to a map from R into M. Depending on the class Q, this concept is both a dualization and a generalization of pure Baer injectivity. We show that every module can be embedded as Q-copure submodule of a Q-copure Baer injective module. Certain types of rings are characterized using properties of Q-copure Baer injective modules. For example a ring R is Q-coregular if and only if every Q-copure Baer injective R-module is injective.