7 papers
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…
On the Diameter and Girth of an Annihilating-Ideal Graph
F. Aliniaeifard, M. Behboodi, E. Mehdi-Nezhad +1
Let be a commutative ring with and be the set of ideals with nonzero annihilators. The annihilating-ideal graph of is defined as the graph $\Bbb{AG}(…
The Annihilating-Ideal Graph of a Ring
F. Aliniaeifard, M. Behboodi, Y. Li
Let be a semigroup with and be a ring with . We extend the definition of the zero-divisor graphs of commutative semigroups to not necessarily commutative semigroups.…
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…