Semisimple-direct-injective modules
The notion of simple-direct-injective modules which are a generalization of injective
modules unifies $ C2 $ and $ C3 $-modules. In the present paper, we introduce the notion of …
modules unifies $ C2 $ and $ C3 $-modules. In the present paper, we introduce the notion of …
[HTML][HTML] Simple-direct-injective modules
A module M over a ring is called simple-direct-injective if, whenever A and B are simple
submodules of M with A≅ B and B⊆⊕ M, we have A⊆⊕ M. Various basic properties of …
submodules of M with A≅ B and B⊆⊕ M, we have A⊆⊕ M. Various basic properties of …
Simple-direct-projective modules
In this paper, we introduce and study the dual notion of simple-direct-injective modules.
Namely, a right R-module M is called simple-direct-projective if, whenever A and B are …
Namely, a right R-module M is called simple-direct-projective if, whenever A and B are …
Characterization of rings using finite-direct-injective modules
In this paper, we characterize strongly right C 2-rings in terms of finite-direct-injective
modules which is a generalization of direct-injective modules (or C 2-modules). Using this …
modules which is a generalization of direct-injective modules (or C 2-modules). Using this …
Simple continuous modules
Y Wang - Hacettepe Journal of Mathematics and Statistics, 2019 - dergipark.org.tr
A module M is called a simple continuous module if it satisfies the conditions (min-C_1) and
(min-C_2). A module M is called singular simple-direct-injective if for any singular simple …
(min-C_2). A module M is called singular simple-direct-injective if for any singular simple …
Rings characterized via some classes of almost-injective modules
In this paper, we study rings with the property that every cyclic module is almost-injective
(CAI). It is shown that R is an Artinian serial ring with J (R)^ 2= 0 J (R) 2= 0 if and only if R is …
(CAI). It is shown that R is an Artinian serial ring with J (R)^ 2= 0 J (R) 2= 0 if and only if R is …
Pure-direct-injective modules
In this paper, we study the class of modules having the property that if any pure submodule
is isomorphic to a direct summand of such a module then the pure submodule is itself a …
is isomorphic to a direct summand of such a module then the pure submodule is itself a …
[PDF][PDF] A generalization of -rings
Y Durğun - Ege Uni. J. of Faculty of Sci, 2013 - Citeseer
Let R be a ring and be a class of right R-modules which is closed under submodules,
quotients and isomorphisms. A right R-module M is called-injective if for every T. A ring R is …
quotients and isomorphisms. A right R-module M is called-injective if for every T. A ring R is …
A generalization of injectivity for modules over a unitary ring
R Yue Chi Ming - Demonstratio Mathematica, 2006 - degruyter.com
In this note, we consider certain generalizations of injectivity and p-injectivity in connection
with von Neumann regular rings, self-injective regular rings, II-regular rings, semi-simple …
with von Neumann regular rings, self-injective regular rings, II-regular rings, semi-simple …