2022/01/24 by Leary, F. C.
#13E05 #Commutative Algebra (math.AC) #FOS: Mathematics #Primary: 13C13 #Secondary: 20K21
paper · doi:10.48550/arxiv.2201.09961
If R is a ring with 1, we call a unital left R-module M co-Hopfian (Hopfian) in the category of left R-modules if any monic (epic) endomorphism of M is an automorphism. For commutative Noetherian R we use results of Matlis to show that in a certain context every submodule of a co-Hopfian injective module is co-Hopfian. For these same R, we characterize when a finitely generated co-Hopfian module has finite length. We describe the structure of Hopfian and co-Hopfian abelian groups whose torsion subgroup is cotorsion.