Add to ORKGIf S is a subnormalizing extension [7] of a ring R with identity generated by a set which is a multiplicative submonoid of S and generates S as a free unital left R-module, then using the left and right module structures of S one can define a set of mappings R → R which satisfy all but (possibly) one of the requirements for a D-structure [2], [3], [4]. It remains unknown whether this remaining condition must in fact be satisfied, but we show that it is satisfied for a number of particular monoids and is at least partially satisfied in general. In the other direction it is known that many but by no means all D-structures are linked to subnormalizing extensions in this way
summary:Lattices of submodules of modules and the operators we can define on these lattices are usef...
It is proved that, for any ring R, a right R-module M has the property that, for every submodule N, ...
In a recent paper, Aydogdu and Lopez-Permouth have defined a module M. to be N-subinjective if every...
If S is a subnormalizing extension [7] of a ring R with identity generated by a set which is a multi...
A D-structure on a ring A with identity is a family of self-mappings indexed by the elements of a mo...
AbstractGiven modules M and N, M is said to be N-subinjective if for every extension K of N and ever...
A module M is called an extending (or CS) module provided that every submodule of M is essential in ...
Because traditional ring theory places restrictive hypotheses on all submodules of a module, its res...
summary:A left module $M$ over an arbitrary ring is called an $\mathcal{RD}$-module (or an $\mathcal...
Let M be a module over a ring R, which satisfies the ascending chain condition on submodules of the ...
AbstractA positive answer is given to the infinite rank four submodules problem. Let λ be an infinit...
A module M is called extending (or CS) if every submodule of M is essential in a direct summand of M...
We study the structure of rings over which every right module is an essential extension of a semisim...
The primary objective of this thesis is to present a unified account of the various generalizations ...
This article introduces the concept of S-semiprime submodules which are a generalization of semiprim...
summary:Lattices of submodules of modules and the operators we can define on these lattices are usef...
It is proved that, for any ring R, a right R-module M has the property that, for every submodule N, ...
In a recent paper, Aydogdu and Lopez-Permouth have defined a module M. to be N-subinjective if every...
If S is a subnormalizing extension [7] of a ring R with identity generated by a set which is a multi...
A D-structure on a ring A with identity is a family of self-mappings indexed by the elements of a mo...
AbstractGiven modules M and N, M is said to be N-subinjective if for every extension K of N and ever...
A module M is called an extending (or CS) module provided that every submodule of M is essential in ...
Because traditional ring theory places restrictive hypotheses on all submodules of a module, its res...
summary:A left module $M$ over an arbitrary ring is called an $\mathcal{RD}$-module (or an $\mathcal...
Let M be a module over a ring R, which satisfies the ascending chain condition on submodules of the ...
AbstractA positive answer is given to the infinite rank four submodules problem. Let λ be an infinit...
A module M is called extending (or CS) if every submodule of M is essential in a direct summand of M...
We study the structure of rings over which every right module is an essential extension of a semisim...
The primary objective of this thesis is to present a unified account of the various generalizations ...
This article introduces the concept of S-semiprime submodules which are a generalization of semiprim...
summary:Lattices of submodules of modules and the operators we can define on these lattices are usef...
It is proved that, for any ring R, a right R-module M has the property that, for every submodule N, ...
In a recent paper, Aydogdu and Lopez-Permouth have defined a module M. to be N-subinjective if every...