Add to ORKGLet R be a ring and M a right R-module. It is shown that (1) δ(M) is Noetherian if and only if M satisfies ACC on δ-small submodules; (2) δ(M) is Artinian if and only if M satisfies DCC on δ-small submodules; (3) M is Artinian if and only if M is an amply δ-supplemented module and satisfies DCC on δ-supplement submodules and on δ-small submodules. Copyright © 2007 Yongduo Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1. Introduction an
In this article, we introduce new classes of submodules called r-submodule and special r-submodule, ...
AbstractWe prove that a ring R is serial if and only if every finitely presented right and left R-mo...
Let M be a module over a ring R, which satisfies the ascending chain condition on submodules of the ...
Let R be a ring and M a right R-module. It is shown that (1) δ(M) is Noetherian if and only if M sat...
It is proved that, for any ring R, a right R-module M has the property that, for every submodule N, ...
It is proved that, for any ring $R$, a right $R$-module $M$ has the property that, for every submodu...
It is proved that, for any ring R, a right R-module M has the property that, for every submodule N, ...
It is proved that, for any ring R, a right R-module M has the property that, for every submodule N, ...
In [9], the author extends the definition of lifting and supplemented modules to ?-lifting and ?-sup...
In[4], Smith and Vedadi characterized modules which satisfy DCC (respectively, ACC) condition on non...
In[4], Smith and Vedadi characterized modules which satisfy DCC (respectively, ACC) condition on non...
We say that a module M satisfies pand-acc provided every submodule with finite uniform dimension is ...
We say that a module M satisfies pand-acc provided every submodule with finite uniform dimension is ...
AbstractA moduleMis known to be a CS-module (or an extending module) if every complement submodule o...
: In this article, we introduce new classes of submodules called r -submodule and special r -submodu...
In this article, we introduce new classes of submodules called r-submodule and special r-submodule, ...
AbstractWe prove that a ring R is serial if and only if every finitely presented right and left R-mo...
Let M be a module over a ring R, which satisfies the ascending chain condition on submodules of the ...
Let R be a ring and M a right R-module. It is shown that (1) δ(M) is Noetherian if and only if M sat...
It is proved that, for any ring R, a right R-module M has the property that, for every submodule N, ...
It is proved that, for any ring $R$, a right $R$-module $M$ has the property that, for every submodu...
It is proved that, for any ring R, a right R-module M has the property that, for every submodule N, ...
It is proved that, for any ring R, a right R-module M has the property that, for every submodule N, ...
In [9], the author extends the definition of lifting and supplemented modules to ?-lifting and ?-sup...
In[4], Smith and Vedadi characterized modules which satisfy DCC (respectively, ACC) condition on non...
In[4], Smith and Vedadi characterized modules which satisfy DCC (respectively, ACC) condition on non...
We say that a module M satisfies pand-acc provided every submodule with finite uniform dimension is ...
We say that a module M satisfies pand-acc provided every submodule with finite uniform dimension is ...
AbstractA moduleMis known to be a CS-module (or an extending module) if every complement submodule o...
: In this article, we introduce new classes of submodules called r -submodule and special r -submodu...
In this article, we introduce new classes of submodules called r-submodule and special r-submodule, ...
AbstractWe prove that a ring R is serial if and only if every finitely presented right and left R-mo...
Let M be a module over a ring R, which satisfies the ascending chain condition on submodules of the ...