3 citations · 4 across the 10 of their papers we have counts for
7 papers · 1 filter
Prime M-Ideals, M-Prime Submodules, M-Prime Radical and M-Baer's Lower Nilradical of Modules
John A. Beachy, Mahmood Behboodi, Faezeh Yazdi
Let M be a fixed left R-module. For a left R-module X, we introduce the notion of M-prime (resp. M-semiprime) submodule of X such that in the case M=R, which coincides with prime (…
Modules Whose Classical Prime Submodules Are Intersections of Maximal Submodules
Marzieh Arabi-Kakavand, Mahmood Behboodi
Commutative rings in which every prime ideal is the intersection of maximal ideals are called Hilbert (or Jacobson) rings. We propose to define classical Hilbert modules by the pro…
Modules Satisfying the Prime Radical Condition and a Sheaf Construction for Modules II
Mansour Aghasi, Mahmood Behboodi, Masoud Sabzevari
In this paper we continue our study of modules satisfying the prime radical condition (-radical modules), that was introduced in Part I (see \cite{BS}). Let be a co…
Modules Satisfying the Prime Radical Condition and a Sheaf Construction for Modules I
Mahmood Behboodi, Masoud Sabzevari
The purpose of this paper and its sequel, is to introduce a new class of modules over a commutative ring , called -radical modules (modules satisfying the prime…
On Commutative Rings Whose Prime Ideals Are Direct Sums of Cyclics
Mahmood Behboodi, Ali Moradzadeh-Dehkordi
In this paper we study commutative rings whose prime ideals are direct sums of cyclic modules. In the case is a finite direct product of commutative local rings, the struct…
On rings each of whose finitely generated modules is a direct sum of cyclic modules
Mahmood Behboodi, Gholamreza Behboodi Eskandari
In this paper we study (non-commutative) rings over which every finitely generated left module is a direct sum of cyclic modules (called left FGC-rings). The commutative case w…
Commutative Local Rings whose Ideals are Direct Sums of Cyclic Modules
Mahmood Behboodi, Seyed Hossain Shojaee
A well-known result of Köthe and Cohen-Kaplansky states that a commutative ring has the property that every -module is a direct sum of cyclic modules if and only if is a…