Modules with many homomorphisms

@article{Smith2005ModulesWM,
  title={Modules with many homomorphisms},
  author={Patrick F. Smith},
  journal={Journal of Pure and Applied Algebra},
  year={2005},
  volume={197},
  pages={305-321}
}
  • Patrick F. Smith
  • Published 1 May 2005
  • Mathematics
  • Journal of Pure and Applied Algebra
ESSENTIALLY RETRACTABLE MODULES
We call a module R M essentially retractable if HomR( ) ,0 MN ≠ for all essential submodules N of M. For a right FBN ring R, it is shown that: (i) A nonzero module R M is retractable (in the sense
WEAK GENERATORS FOR CLASSES OF R-MODULES
Let R be a ring. An R-module M is called a weak generator for a class C of R-modules if Hom_R(M,V) is non-zero for every non-zero module V in C. A projective module M is a weak generator for C if and
Rings whose non-zero finitely generated modules are retractable
We give several equivalent formulations of a finite retractable ring which is defined to be a ring R, all of whose non-zero finitely generated (right) modules M are retractable, in the sense that
RINGS WITH ALL FINITELY GENERATED MODULES RETRACTABLE
Several characterizations of a ring R is given for which any non-zero finitely generated module M is retractable in the sense that HomR(M,N) is non-zero whenever N is a non-zero submodule of M. Such
On rings whose modules have nonzero homomorphisms to nonzero submodules
We carry out a study of rings R for which HomR (M;N) 6= 0 for all nonzero N ≤ MR. Such rings are called retractable. For a retractable ring, Artinian condition and having Krull dimension are
Applications of epi-retractable modules
An R-module M is called epi-retractable if every sub- module of MR is a homomorphic image of M. It is shown that if R is a right perfect ring, then every projective slightly compress- ible module MR
EPI-Retractable Modules and Some Applications
Generalizing concepts "right Bezout " and "principal right ideal " of a ring R to modules, an R-module M is called n-epi- retractable (resp. epi-retractable) if every n-generated submodule (resp.
Study of Subhomomorphic Property to a Ring
Let M and N be two non-zero right R-modules, M is called subhomomorphic to N in case there exist R homomorphisms f : M ! N, g : N ! M such that gof is non-zero, and M is called strongly
BOUNDED AND FULLY BOUNDED MODULES
Abstract Generalizing the concept of right bounded rings, a module MR is called bounded if annR(M/N)≤eRR for all N≤eMR. The module MR is called fully bounded if (M/P) is bounded as a module over
Some Results on C-retractable Modules
TLDR
It is shown that every projective module over a right SI-ring is c-retractable and that a locally noetherian c- retractable module is homo-related to a direct sum of uniform modules.
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