Annsemimaximal and Coannsemimaximal Modules
: Annsemimaximal module
semisimple module
semisimple ring
semiprime module
max-module
uniform module
Z-regular module
F-regular module
Artinian module
flat module
coprime module
coannsemimaximal module.
Some authors studied modules with annihilator of every nonzero submodule is prime, primary or maximal. In this paper, we introduce and study annsemimaximal and coannsemimaximal modules, where an R-module M is called annsemimaximal (resp. coannsemimaximal) if annRN (resp. ) is semimaximal ideal of R for each nonzero submodule N of M.