3 citations · 4 across the 10 of their papers we have counts for
16 papers
Left Co-Köthe Rings and Their Characterizations
Shadi Asgari, Mahmood Behboodi, Somayeh Khedrizadeh
Köthe's classical problem posed by G. Köthe in 1935 asks to describe the rings such that every left -module is a direct sum of cyclic modules (these rings are known as left…
Several Characterizations of Left Köthe Rings
Shadi Asgari, Mahmood Behboodi, Somayeh Khedrizadeh
We study the classical Köthe's problem, concerning the structure of non-commutative rings with the property that: ``every left module is a direct sum of cyclic modules". In 1934, K…
-semi-compact rings and modules
Mahmood Behboodi, François Couchot, Seyed Hossein Shojaee
In this paper several characterizations of semi-compact modules are given. Among other results, we study rings whose semi-compact modules are injective. We introduce the property $…
Two Generalizations of the Wedderburn-Artin Theorem with Applications
Mahmood Behboodi, Asghar Daneshvar, Mohammad Reza Vedadi
We say that an -module is {\it virtually simple} if and for every non-zero submodule of , and {\it virtually semisimple} if each submodule of $…
Virtually Semisimple Modules and a Generalization of the Wedderburn-Artin Theorem
Mahmood Behboodi, Asghar Daneshvar, Mohammad Reza Vedadi
By any measure, semisimple modules form one of the most important classes of modules and play a distinguished role in the module theory and its applications. One of the most fundam…
Noetherian Rings Whose Annihilating-Ideal Graphs Have finite Genus
Farid Aliniaeifard, Mahmood Behboodi, Yuanlin Li
Let be a commutative ring and be the set of ideals with non-zero annihilators. The annihilating-ideal graph of is defined as the graph with v…
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…
Rings Whose Annihilating-Ideal Graphs Have Positive Genus
Farid Aliniaeifard, Mahmood Behboodi
Let be a commutative ring and be the set of ideals with non-zero annihilators. The annihilating-ideal graph of is defined as the graph with t…
The Annihilating-Ideal Graph of Commutative Rings II
Mahmood Behboodi, Zahra Rakeei
In this paper we continue our study of annihilating-ideal graph of commutative rings, that was introduced in Part I (see [5]). Let be a commutative ring with its…
The Annihilating-Ideal Graph of Commutative Rings I
Mahmood Behboodi, Zahra Rakeei
Let be a commutative ring with its set of ideals with nonzero annihilator. In this paper and its sequel, we introduce and investigate the {\it annihilating-ideal…