HEREDITARY AND SEMIHEREDITARY REPRESENTATIONS OF QUIVERS

Bennis, Driss,Roudi, Adnane Korean Mathematical Society 2021 대한수학회보 Vol.58 No.6

In this paper, we investigate hereditary and semihereditary representations of quivers over an arbitrary ring. As consequences hereditary and semihereditary category of representations of quivers over an arbitrary ring are characterized.

ON GENERALIZED GRADED CROSSED PRODUCTS AND KUMMER SUBFIELDS OF SIMPLE ALGEBRAS

Bennis, Driss,Mounirh, Karim,Taraza, Fouad Korean Mathematical Society 2019 대한수학회보 Vol.56 No.4

Using generalized graded crossed products, we give necessary and sufficient conditions for a simple algebra over a Henselian valued field (under some hypotheses) to have Kummer subfields. This study generalizes some known works. We also study many properties of generalized graded crossed products and conditions for embedding a graded simple algebra into a matrix algebra of a graded division ring.

EXTENDED ZERO-DIVISOR GRAPHS OF IDEALIZATIONS

Bennis, Driss,Mikram, Jilali,Taraza, Fouad Korean Mathematical Society 2017 대한수학회논문집 Vol.32 No.1

Let R be a commutative ring with zero-divisors Z(R). The extended zero-divisor graph of R, denoted by $\bar{\Gamma}(R)$, is the (simple) graph with vertices $Z(R)^*=Z(R){\backslash}\{0\}$, the set of nonzero zero-divisors of R, where two distinct nonzero zero-divisors x and y are adjacent whenever there exist two non-negative integers n and m such that $x^ny^m=0$ with $x^n{\neq}0$ and $y^m{\neq}0$. In this paper, we consider the extended zero-divisor graphs of idealizations $R{\ltimes}M$ (where M is an R-module). At first, we distinguish when $\bar{\Gamma}(R{\ltimes}M)$ and the classical zero-divisor graph ${\Gamma}(R{\ltimes}M)$ coincide. Various examples in this context are given. Among other things, the diameter and the girth of $\bar{\Gamma}(R{\ltimes}M)$ are also studied.

ON S-COHERENCE

Bennis, Driss,El Hajoui, Mohammed Korean Mathematical Society 2018 대한수학회지 Vol.55 No.6

Recently, Anderson and Dumitrescu's S-finiteness has attracted the interest of several authors. In this paper, we introduce the notions of S-finitely presented modules and then of S-coherent rings which are S-versions of finitely presented modules and coherent rings, respectively. Among other results, we give an S-version of the classical Chase's characterization of coherent rings. We end the paper with a brief discussion on other S-versions of finitely presented modules and coherent rings. We prove that these last S-versions can be characterized in terms of localization.

ON JORDAN IDEALS IN PRIME RINGS WITH GENERALIZED DERIVATIONS

Bennis, Driss,Fahid, Brahim,Mamouni, Abdellah Korean Mathematical Society 2017 대한수학회논문집 Vol.32 No.3

Let R be a 2-torsion free prime ring and J be a nonzero Jordan ideal of R. Let F and G be two generalized derivations with associated derivations f and g, respectively. Our main result in this paper shows that if F(x)x - xG(x) = 0 for all $x{\in}J$, then R is commutative and F = G or G is a left multiplier and F = G + f. This result with its consequences generalize some recent results due to El-Soufi and Aboubakr in which they assumed that the Jordan ideal J is also a subring of R.

On $S$-coherence

Driss Bennis,Mohammed El Hajoui 대한수학회 2018 대한수학회지 Vol.55 No.6

Recently, Anderson and Dumitrescu's $S$-finiteness has attracted the interest of several authors. In this paper, we introduce the notions of $S$-finitely presented modules and then of $S$-coherent rings which are $S$-versions of finitely presented modules and coherent rings, respectively. Among other results, we give an $S$-version of the classical Chase's characterization of coherent rings. We end the paper with a brief discussion on other $S$-versions of finitely presented modules and coherent rings. We prove that these last $S$-versions can be characterized in terms of localization.

On generalized graded crossed products and Kummer subfields of simple algebras

Driss Bennis,Karim Mounirh,Fouad Taraza 대한수학회 2019 대한수학회보 Vol.56 No.4

Using generalized graded crossed products, we give necessary and sufficient conditions for a simple algebra over a Henselian valued field (under some hypotheses) to have Kummer subfields. This study generalizes some known works. We also study many properties of generalized graded crossed products and conditions for embedding a graded simple algebra into a matrix algebra of a graded division ring.

Ultra Dense Small Cell Networks: Turning Density Into Energy Efficiency

Samarakoon, Sumudu,Bennis, Mehdi,Saad, Walid,Debbah, Merouane,Latva-aho, Matti IEEE 2016 IEEE journal on selected areas in communications Vol.34 No.5

<P>In this paper, a novel approach for joint power control and user scheduling is proposed for optimizing energy efficiency (EE), in terms of bits per unit energy, in ultra dense small cell networks (UDNs). Due to severe coupling in interference, this problem is formulated as a dynamic stochastic game (DSG) between small cell base stations (SBSs). This game enables capturing the dynamics of both the queues and channel states of the system. To solve this game, assuming a large homogeneous UDN deployment, the problem is cast as a mean-field game (MFG) in which the MFG equilibrium is analyzed with the aid of low-complexity tractable partial differential equations. Exploiting the stochastic nature of the problem, user scheduling is formulated as a stochastic optimization problem and solved using the drift plus penalty (DPP) approach in the framework of Lyapunov optimization. Remarkably, it is shown that by weaving notions from Lyapunov optimization and mean-field theory, the proposed solution yields an equilibrium control policy per SBS, which maximizes the network utility while ensuring users' quality-of-service. Simulation results show that the proposed approach achieves up to 70.7% gains in EE and 99.5% reductions in the network's outage probabilities compared to a baseline model, which focuses on improving EE while attempting to satisfy the users' instantaneous quality-of-service requirements.</P>

JORDAN 𝒢_n-DERIVATIONS ON PATH ALGEBRAS

Adrabi, Abderrahim,Bennis, Driss,Fahid, Brahim Korean Mathematical Society 2022 대한수학회논문집 Vol.37 No.4

Recently, Brešar's Jordan {g, h}-derivations have been investigated on triangular algebras. As a first aim of this paper, we extend this study to an interesting general context. Namely, we introduce the notion of Jordan 𝒢_n-derivations, with n ≥ 2, which is a natural generalization of Jordan {g, h}-derivations. Then, we study this notion on path algebras. We prove that, when n > 2, every Jordan 𝒢_n-derivation on a path algebra is a {g, h}-derivation. However, when n = 2, we give an example showing that this implication does not hold true in general. So, we characterize when it holds. As a second aim, we give a positive answer to a variant of Lvov-Kaplansky conjecture on path algebras. Namely, we show that the set of values of a multi-linear polynomial on a path algebra KE is either {0}, KE or the space spanned by paths of a length greater than or equal to 1.

Dynamic Clustering and <small>on</small>/<small>off</small> Strategies for Wireless Small Cell Networks

Samarakoon, Sumudu,Bennis, Mehdi,Saad, Walid,Latva-aho, Matti IEEE 2016 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS Vol.15 No.3

<P>In this paper, a novel cluster-based approach for maximizing the energy efficiency of wireless small cell networks is proposed. A dynamic mechanism is proposed to locally group coupled small cell base stations (SBSs) into clusters based on location and traffic load. Within each formed cluster, SBSs coordinate their transmission parameters to minimize a cost function, which captures the tradeoffs between energy efficiency and flow level performance, while satisfying their users' quality-of-service requirements. Due to the lack of intercluster communications, clusters compete with one another to improve the overall network's energy efficiency. This intercluster competition is formulated as a noncooperative game between clusters that seek to minimize their respective cost functions. To solve this game, a distributed learning algorithm is proposed using which clusters autonomously choose their optimal transmission strategies based on local information. It is shown that the proposed algorithm converges to a stationary mixed-strategy distribution, which constitutes an epsilon-coarse correlated equilibrium for the studied game. Simulation results show that the proposed approach yields significant performance gains reaching up to 36% of reduced energy expenditures and upto 41% of reduced fractional transfer time compared to conventional approaches.</P>