  ABSTRACT ALGEBRA
One day conference
Faculty os Science, Alexandria University
July 26, 2016, Egypt
 
   



 المؤتمر على روح المغفور لهما الدكتور محمد رفعت عبد السلام والدكتور جمال عبد اللطيف  جامعة سوهاج
 The Deadlines For Registration has been Postponed Till 15 Jan 2016
List of Abstracts












 
Title:Asymmetric threeplayer prisoner's dilemma game  Author Information Name:  Karim Mohamed Soliman  University/Institute:  Zewail City for Science and Technology  Email:  kamohamed@zewailcity.edu.eg 
 Abstract: Although most game theory researches on the prisoner's dilemma have centered on twoplayer models, it is possible to create it to be consisted of three or even more players. In this article, we are interested in the model of threeplayer iterated prisoner's dilemma game where, each player has only two choices. The action of each strategy in this model depends on the previous action of the last round. Each strategy is presented by finite state of automata. We used a computer program to calculate the payoff values resulting from the actions of all possible strategies, and studied the behavior of different four strategies related to the Tit for Tat concept in order to determine the conditions of each strategy to be the best. However the asymmetric games need more advanced computations than the symmetric games, we supposed an agreement between two players against the third player by choosing either to cooperate together or to defect together at each round. According to that assumption, the game is transformed from the symmetric threeplayer model to asymmetric twoplayer model such that, the identities of the players cannot be interchanged without interchanging the payoff of the strategies. We determined the payoff matrix corresponding to the all possible strategies, and noticed that for some strategies, it is better to be a player of the first type (independent player) than being of the second type (allies). In appendix section, we designed an algorithm and implement it using the Java programming language to facilitate the calculations.   
Title:New exact solutions for the higher  order long water  wave equations by using ( G^'/G ,1/G ) expansion method  Author Information Name:  E.E. Eladdad_  University/Institute:  Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt.  Email:  elsayedeladdad@yahoo.com 
 Abstract: In this paper the ( G^'/G ,1/G )  expansion method with the aid of Mathematica are used to obtain new exact solutions of the nonlinear partial differential equations. The travelling wave solutions are expressed by the hyperbolic functions, the trigonometric functions and the rational function. As application, the exact solutions of higher  order long water  wave equations [1] are obtained.   
Title:Analytical solution of a boundaryvalue problem in the frame of second gradient elastic deformation for anisotropic materials in a rectangular domain  Author Information Name:  A. R. El Dhaba  University/Institute:  Damanhour University, Faculty of Science.  Email:  amrramadaneg@yahoo.com 
 Abstract: Abstract:
A semiinverse method is used to find analytical solutions for a plane boundaryvalue problem of linear anisotropic elastic material, in the frame of the second gradient deformation and for a rectangular domain. The solution for the displacement components are expressed as finite sums of elementary functions, with coefficients determined from the boundary conditions, that are imposed in integral form. Two examples are presented for a rectangle subjected to either normal and shear deformation. According to the method that is exploited, the boundary conditions are imposed in integral form.   
Title:Weakly Primary Submodules over Noncommutative Rings  Author Information Name:  Arwa Eid Ashoura,  University/Institute:  Department of Mathematics, The Islamic University of Gaza, Gaza, Palestine.  Email:  arashour@iugaza.edu.ps 
 First Additional Author Information Name:  Mohammad Hamodab  University/Institute:  Department of Mathematics,The Islamic University of Gaza, Gaza, Palestine.  Email:  aboood 7373@hotmail.com 
 Abstract: Let R be an associative ring with nonzero identity and let M be a unitary left
R−module. In this paper, we introduce the concept of weakly primary submodules
of M and give some basic properties of these classes of submodules. Several
results on weakly primary submodules over noncommutative rings are proved. We
show that N is a weakly primary submodule of a left R−module M iff for every
ideal P of R and for every submodule D of M with 0 ̸= PD ⊆ N; either
P ⊆
√
(N : M) or D ⊆ N: We also introduce the definitions of weakly primary
compactly packed and maximal compactly packed modules. Then we study the relation
between these modules and investigate the condition on a left R−module M
that makes the concepts of primary compactly packed modules and weakly primary
compactly packed modules equivalent. We also introduce the concept of weakly
primary radical submodules and show that every Bezout module that satisfies the
ascending chain condition on weakly primary radical submodules is weakly primary
compactly packed module.   
Title:The family of right N_semilocal rings  Author Information Name:  Samia Mohamed Abelwahab  University/Institute:  Helwan university  Email:  dr.samiamohamed.n@gmail.com 
 First Additional Author Information Name:  Mohamed H. Fahmy  University/Institute:  Al_ Azhar university  Email:  d_ mfahmy@ yahoo.com 
 Second Additional Author Information Name:  Abdelrahman Mohamed Hasanen  University/Institute:  Al_Azhar university  Email:  
 Abstract: In this paper we extend the notion of semilocal rings, giving the properties of the family of right and left N_semilocal rings. We give examples to show that these classes are proper subclasses of the family of local rings and right Noetherian rings.   
Title:McCoy property over prime Radicals  Author Information Name:  Shaimaa Shehata Hussein Shehata  University/Institute:  Assistant teacher, faculty of science, AlAzhar university  Email:  shaimaa.sh_math@yahoo.com 
 First Additional Author Information Name:  Mohammad Hussein Fahmy  University/Institute:  professor, faculty of science, AlAzhar university  Email:  d_mfahmy@yahoo.com 
 Second Additional Author Information Name:  Refaat Mohammad Salem  University/Institute:  professor, faculty of science, AlAzhar university  Email:  rsalem_@hotmail.com 
 Abstract: abstract
In this paper we study McCoy rings over prime radicals(MPR) which generalize McCoy rings and armendariz rings over prime radicals and investigate their properties. The structure and several kinds of extensions of MPR rings are investigated.   
Title:A study of some properties of modules related to annihilators  Author Information Name:  Fatma Azmy  University/Institute:  Faculty of Science, AlAzhar University  Email:  fatema_azmy@hotmail.com 
 First Additional Author Information Name:  S. T. Rizvi  University/Institute:  Department of Mathematics, The Ohio State University, Ohio, Lima, USA  Email:  rizvi.1@osu.edu 
 Second Additional Author Information Name:  C. Roman  University/Institute:  Department of Mathematics, The Ohio State University, Ohio, Lima, USA  Email:  
 Abstract: Extending a result of Chatters and Khuri (1980) to the module theoretic setting, Rizvi and Roman showed that "a module $M$ is $mathcal{K}$nonsingular and extending if and if $M$ is $mathcal{K}$cononsingular and Baer". This result shows that the notion of an extending module is closely linked to that of a Baer module. Recall that a right $R$module $M$ is called Baer if for all $Nleq M$, $l_S (N ) leq^oplus {}_{S}S$ where $S = End_R (M)$. Further, $M_R$ is called $mathcal{K}$nonsingular if $forall varphi in S$ such that $Ker varphi leq^e M$, $varphi = 0$. $M_R$ is called $mathcal{K}$cononsingular if for any $Nleq M$ with $varphi N
eq 0$ $forall$ $varphi in S$, then $Nleq^e M$. Equivalently, if $N
leq^e M$, then $exists$ $0
eq varphi in S$ such that $varphi N =0$. While the notion of $mathcal{K}$nonsingular modules has been studied earlier, not much is known about $mathcal{K}$cononsingular modules to the best of our knowledge. In this talk we investigate $mathcal{K}$cononsingular modules and a related slightly stronger condition.   
Title:HOMOGENEOUS SEMILOCAL PROPERTY OF CORNER RINGS AND NJRINGS  Author Information Name:  Susan F. ElDeken  University/Institute:  Helwan University  Email:  Sfdeken@hotmail.com 
 First Additional Author Information Name:  Susan F. ElDeken  University/Institute:  Helwan University  Email:  Sfdeken@hotmail.com 
 Second Additional Author Information Name:  A. Ageeb  University/Institute:  AlAzhar University  Email:  
 Abstract: Abstract. Let be the Jacobson radical of a ring R. A ring R is said to be homogeneous semilocal ring if is simple artinian. We construct examples of corner rings eRe which are homogeneous semilocal but their base rings are not and determine under what conditions this property transferred. A ring R is said to be NJring if every element of RJ is regular. Homogeneous semilocal rings and NJrings are generalizations of local rings. Several properties of the homogeneous semilocal NJrings are studied. The regularity of homogeneous semilocal rings is investigated as well.   
Title:On weakly H –embedded subgroups of finite groups  Author Information Name:  M. Asaad and M.Ramadan  University/Institute:  Cairo University Faculty of Science Department of Mathematics  Email:  mramadan12@yahoo.com 
 Abstract: Let G be a finite group. A subgroup H of G is called an H –subgroup in G if NG(H) Ç Hg £ H for all gÎG. A subgroup H of G is called weakly H –subgroup in G if there exists a normal subgroup K of G such that G = HK and H Ç K is an H –subgroup in G. We say that a subgroup H of G is weakly H –embedded in G if there exists a normal subgroup K of G such that HG = HK and H Ç K is an H –subgroup in G. In this work, we investigate the structure of the finite group G under that the assumption that certain subgroups of prime power order are weakly H –embedded in G. Our results improve and generalize several results in the literature.   
Title:Some algebraic properties of generalized power series rings  Author Information Name:  R. M. Salem  University/Institute:  Fac. Science AlAzhar Univ.  Email:  Refaat_salem@ciccairo.com 
 Abstract: Abstract: In 1989, Carl Faith introduced the notion of the zero intersection property (zip) on annihilators of a ring R. A ring ııRı ıis called a ııııright zip ring if whenever the right annihilator of a subset ıXıı of ıRıı vanishes, then there exists a finite subset ıY of X ısuch that r_R (Y)=0, equivalently, for a left ideal ıLı of ıRı with r_R L=0,there exists a finitely generated left ideal T contained in Lıı such that r_R T=0. The definition a left zip ring follows similarly. In recent years, several algebraists have been interested in study of the zip and weak zip properties and their behavior in ring extensions. The purpose of this talk is to present the progress of work on these properties in different ring extensions, especially in skew generalized (and generalized) power series rings.   
Title:Graph Isomorphism and Automorphism Groups  Author Information Name:  Atef mohamed AboElkher  University/Institute:  Assiut University  Email:  atefmohamed55@yahoo.com 
 First Additional Author Information Name:  Essam El Seidy  University/Institute:  Department of Mathematics, Faculty of Science, Ain Shams University, Abbassia, Cairo, Egypt  Email:  esam_elsedy@hotmail.com 
 Second Additional Author Information Name:  Salah ElDin Hussein  University/Institute:  Department of Mathematics, Faculty of Science, Ain Shams University, Abbassia, Cairo, Egypt  Email:  mynsalah@hotmail.com 
 Third Additional Author Information Name:  Atef AboElkher  University/Institute:  Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt  Email:  atefmohamed55@yahoo.com 
 Abstract: An algebraic approach to graph theory can be useful in numerous ways. There is a relatively natural intersection between the ﬁelds of algebra and graph theory, speciﬁcally between group theory and graphs. Perhaps the most natural connection between group theory and graph theory lies in ﬁnding the automorphism group of a given graph. However, by studying the opposite connection, that is, ﬁnding a graph of a given group, we can deﬁne an extremely important family of vertextransitive graphs. In this chapter explores the structure of these graphs and the ways in which we can use groups to explore their properties.   
Title:PARTIAL ACTIONS OF CLIFFORD SEMIGROUPS  Author Information Name:  Ahmed Ageeb Elokl  University/Institute:  Math. Dept. Fac. of Sci., AlAzhar Univ., Nasr city (11884), Cairo, Egypt.  Email:  ahmadageb@yahoo.com 
 First Additional Author Information Name:  M. H. FAHMY  University/Institute:  Math. Dept. Fac. of Sci., AlAzhar Univ., Nasr city (11884), Cairo, Egypt.  Email:  d_mfahmy@yahoo.com 
 Second Additional Author Information Name:  A. M. HASSANEIN  University/Institute:  Math. Dept. Fac. of Sci., AlAzhar Univ., Nasr city (11884), Cairo, Egypt.  Email:  
 Third Additional Author Information Name:  Refaat Mohamed Salem  University/Institute:  Math. Dept. Fac. of Sci., AlAzhar Univ., Nasr city (11884), Cairo, Egypt.  Email:  
 Abstract: Given a partial group G; we constract, in a canonical way, an inverse semigroup S(G) associated to G. The actions of S(G) are shown to be in one to one correspondence with the partial actions of G. This
extend a result of R. Exel [4] who gave the same correspondance for a group G.   
  
   

