Add to ORKGTwo methods of generalizing the classical Noetherian theory to modules over arbitrary rings are described in detail. The first is by extending the primary ideals and isolated components of Murdoch to modules. The second is by using the tertiary sub-modules of Lesieur and Croisot. The development is self-contained except for elementary notions of ring and module theory. The definition of primal submodules with some results is included for completeness. Some concrete examples are given as illustrations.Science, Faculty ofMathematics, Department ofGraduat
It is proved that, for any ring $R$, a right $R$-module $M$ has the property that, for every submodu...
Parkash and Kour obtained a new version of Cohen's theorem for Noetherian modules, which states that...
AbstractIn this paper I present definitions and algorithms for Gröbner bases for submodules of free ...
Abstract. We show that finitely generated modules over a commu-tative Noetherian ring can be classif...
In this paper, we study primary decomposition of any proper submodule N of a module M over a noether...
In this paper, we study primary decomposition of any proper submodule N of a module M over a noether...
It is proved that, for any ring R, a right R-module M has the property that, for every submodule N, ...
AbstractA moduleMis known to be a CS-module (or an extending module) if every complement submodule o...
It is proved that, for any ring R, a right R-module M has the property that, for every submodule N, ...
subcategory noethA which is formed by all noetherian A-modules. An A-module is locally noetherian if...
It is proved that, for any ring R, a right R-module M has the property that, for every submodule N, ...
I introduce a class of totally transcendental (tt) theories called basic and prove a structure theor...
This thesis examines the structure of injective modules over commutative noetherian rings. The autho...
Let M be a module over a ring R, which satisfies the ascending chain condition on submodules of the ...
The concepts of prime ideals and prime modules were introduced over noncommutative rings. In this ar...
It is proved that, for any ring $R$, a right $R$-module $M$ has the property that, for every submodu...
Parkash and Kour obtained a new version of Cohen's theorem for Noetherian modules, which states that...
AbstractIn this paper I present definitions and algorithms for Gröbner bases for submodules of free ...
Abstract. We show that finitely generated modules over a commu-tative Noetherian ring can be classif...
In this paper, we study primary decomposition of any proper submodule N of a module M over a noether...
In this paper, we study primary decomposition of any proper submodule N of a module M over a noether...
It is proved that, for any ring R, a right R-module M has the property that, for every submodule N, ...
AbstractA moduleMis known to be a CS-module (or an extending module) if every complement submodule o...
It is proved that, for any ring R, a right R-module M has the property that, for every submodule N, ...
subcategory noethA which is formed by all noetherian A-modules. An A-module is locally noetherian if...
It is proved that, for any ring R, a right R-module M has the property that, for every submodule N, ...
I introduce a class of totally transcendental (tt) theories called basic and prove a structure theor...
This thesis examines the structure of injective modules over commutative noetherian rings. The autho...
Let M be a module over a ring R, which satisfies the ascending chain condition on submodules of the ...
The concepts of prime ideals and prime modules were introduced over noncommutative rings. In this ar...
It is proved that, for any ring $R$, a right $R$-module $M$ has the property that, for every submodu...
Parkash and Kour obtained a new version of Cohen's theorem for Noetherian modules, which states that...
AbstractIn this paper I present definitions and algorithms for Gröbner bases for submodules of free ...