Modules whose ec-closed submodules are direct summand
A module $ M $ is called ECS if every ec-closed submodule of $ M $ is a direct summand. It
was shown that the ECS property lies strictly between CS and P-extending properties. We …
was shown that the ECS property lies strictly between CS and P-extending properties. We …
On U-torsionless modules and U-neat modules
X Lin, W Chunjin - East West Math, 2000 - eastwestmath.org
Using U-torsionless module we characterize U-neat submodules and Au-injective modules.
If M is a left R-module, U is E (M)-injective and Eu (M)/M does not contain a nonzero …
If M is a left R-module, U is E (M)-injective and Eu (M)/M does not contain a nonzero …
[PDF][PDF] Addendum to “Exact embedding functors between categories of modules”
G Hutchinson - Journal of Pure and Applied Algebra, 1987 - core.ac.uk
(1) There exists an exact embedding functor R-Mod~ S-Mod.(2) There exists a bimodule
sAR such that AR is faithfully flat.(3) There exists a bimodule sBR with BR a (nontrivial) free …
sAR such that AR is faithfully flat.(3) There exists a bimodule sBR with BR a (nontrivial) free …
An alternative perspective on flatness of modules
Y Durğun - Journal of Algebra and Its Applications, 2016 - World Scientific
Given modules RM and AR, RM is said to be absolutely AR-pure if A⊗ M→ A⊗ B is a
monomorphism for every extension RB of RM. For a module AR, the absolutely pure domain …
monomorphism for every extension RB of RM. For a module AR, the absolutely pure domain …
Relative Tor functors with respect to a semidualizing module
Let C be a semidualizing module over a commutative noetherian ring R. We exhibit an
isomorphism Tor^F_CM_i(-,-)≅Tor^P_CM_i(-,-) between the bifunctors defined via C-flat and …
isomorphism Tor^F_CM_i(-,-)≅Tor^P_CM_i(-,-) between the bifunctors defined via C-flat and …
[HTML][HTML] Serre's vanishing conjecture for Ext-groups
I Mori - Journal of Pure and Applied Algebra, 2004 - Elsevier
Let R be a noetherian commutative local ring, and M, N be finitely generated R-modules.
Then a generalized form of Serre's Vanishing conjecture can be stated as follows: if then …
Then a generalized form of Serre's Vanishing conjecture can be stated as follows: if then …
On the existence of covers by injective modules relative to a torsion theory
JR García Rozas, B Torrecillas - Communications in algebra, 1996 - Taylor & Francis
Let R be a ring with identity. In this note we study covers of left R-modules by r-injectives left
R-modules, where r is a hereditary torsion theory defined in the category of all left R …
R-modules, where r is a hereditary torsion theory defined in the category of all left R …
An alternative perspective on pure-projectivity of modules
The study of pure-projectivity is accessed from an alternative point of view. Given modules M
and N, M is said to be N-pure-subprojective if for every pure epimorphism g: B → N g: B→ N …
and N, M is said to be N-pure-subprojective if for every pure epimorphism g: B → N g: B→ N …
Injective modules under faithfully flat ring extensions
L Christensen, F Köksal - Proceedings of the American Mathematical …, 2016 - ams.org
Let $ R $ be a commutative ring and let $ S $ be an $ R $-algebra. It is well-known that if $ N
$ is an injective $ R $-module, then $\operatorname {Hom} _R (S, N) $ is an injective $ S …
$ is an injective $ R $-module, then $\operatorname {Hom} _R (S, N) $ is an injective $ S …
F-projectivity and flat epimqrphisms
MF Jones - Communications in Algebra, 1981 - Taylor & Francis
Let cp be a ring homomorphism from a ring R to a ring Q. If Q is flat as a right R-module and
q is a ring epimorphism, we say that QR is a flat epimorphism. If Q is projective with respect …
q is a ring epimorphism, we say that QR is a flat epimorphism. If Q is projective with respect …