International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Algebra and applications.

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Jordan quadruple systems with quadripotents

Hader A. Elgendy

Damietta University

ABSTRACT

The purpose of this paper is to extend the notations of the compatibility and orthogonality of tripotents in a Jordan triple system to that of quadripotents in a Jordan quadruple system. We provide the necessary and sufficient condition for the compatibility of quadripotents in a Jordan quadruple system. Moreover, we refine the Peirce decomposition of Jordan quadruple systems to be with respect to a system of orthogonal quadripotents and get the multiplication rules of the Peirce spaces. We also study the relation between minimal and primitive quadripotents in a Jordan quadruple system. Finally, we show that from any Jordan quadruple system with a quadripotent, we can define a Jordan algebra.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

It is shown that a particular classes of heterotypical semigroup identities whose both sides contain repeated variables and are preserved under epis in conjunction with all seminormal identities using Isbell's Zigzag Theorem.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Algebra and applications.

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Finite groups with certain kind of subgroups weakly c-supplemented

Mohamed Asaad , Abdelrahman Heliel

Department of Mathematics, Faculty of Science, Cairo University, Giza, 12613, Egypt

Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, 62511, Egypt

ABSTRACT

Let G be a finite group. A subgroup H of G is called an H-subgroup in G if NG(H)∩Hg ≤ H for every g belongs to G. A subgroup H of G is called weakly c-supplemented in G if G has a subgroup K such that G = HK and H∩K is an H-subgroup in G. In this talk, we investigate the structure of finite groups by means of weakly c-supplemented subgroups. Some recent results about supersolvability of finite groups are generalized to a saturated formation containing the class of all supersolvable groups.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Algebra and applications.

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An Operation on Intuitionistic Fuzzy Matrices

E.G.Emam

Department of Mathematics,Faculty of Science, Zagazig University

ABSTRACT

In this paper, we define an operation on the intuitionistic fuzzy matrices called the Gödel implication operator as an extension to the definition of this operator in the case of ordinary fuzzy matrices due to Sanchez and Hashimoto. Using this operator, we prove several important results for intuitionistic fuzzy matrices. Particularly, some properties concerning pre-orders, sub-inverses, and regularity . We concentrate our discussion on the reflexive and transitive matrices. This studying enables us to give a largest sub-inverse and a largest generalized inverse for a reflexive and transitive intuitionistic fuzzy matrix. Also, we obtain an idempotent intuitionistic fuzzy matrix from any given one .

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Algebra and applications.

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EXTENSIONS OF HOMOGENEOUS SEMILOCAL RINGS I

SUSAN F. EL-DEKEN

Department of Mathematics Faculty of Science, Helwan University Ain Helwan, 11790, Helwan, Egypt

ABSTRACT

A ring R with Jacobson radical J(R) is a homogeneous semilocal ring if R/J(R) is simple
artinian. In this paper, we study the transfer of the property of being homogeneous
semilocal from a ring R to the formal power series ring R[[x]], the skew formal power
series ring R[[x, α]] and the Hurwitz series ring HR. The results of the paper generalize
those proved for commutative local rings. We also consider finite centralizing extensions
proving that if the ring of matrices M n (R) is a homogeneous semilocal ring, then so
is R. More generally, if e is an idempotent of a homogeneous semilocal ring S, then eSe
is homogeneous semilocal.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Algebra and applications.

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Non-commutative Unique Factorization Rings with Zero Divisors

M. H. Fahmy , A. M. Hassanian , A. Naser

Math. Dept., Fac. of Sci., Al-Azhar Univ., Nasr city (11884), Cairo, Egypt.

Math. Dept., Fac. of Sci., Al-Azhar Univ., Nasr city (11884), Cairo, Egypt.

Math. Dept., Fac. of Women, Ain Shams Univ., Nasr city (Fax:24157804), Cairo, Egypt.

ABSTRACT

It was shown by Galovich that if R is commutative UFR with identity, then the set of non-units in R is nilpotent, and R is local. In this paper we extend Galovich's results in non-commutative UFR.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Algebra and applications.

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Radicals-domain and their generalizations

Mohamed H. Fahmy , Sabria Atallah , Abdel-Rahman Hassanein , Sarah Kamal El-Din

Prof. of Math. Math. Dept., Faculty of Science, Al-Azhar University, Cairo, Egypt.

Prof. of Math. Math. Dept., Faculty of Science(Girls), Al-Azhar University, Cairo, Egypt.

Prof. of Math. Math. Dept., Faculty of Science, Al-Azhar University, Cairo, Egypt.

Ass.teacher. of Math. Math. Dept., Faculty of Science (Girls), Al-Azhar University, Cairo, Egypt.

ABSTRACT

This paper is two folded. One consider a well known series of generalization of domains such as reduced, symmetric, reversible,...,dedekind finite. The other consider the extension of those rings by their radicals, concentrating on prime and Jacobson radicals. We study their structure and deduce by examples that such rings are not related.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Algebra and applications.

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Weierstrass points of order one on smooth septic curves

Mohammed A. Saleem , Waleed Khaled Elshareef

Sohag University, Egypt.

Sohag University, Egypt.

ABSTRACT

Weierstrass points on an algebraic curve C of genus g≥2, as well as their generalizations to higher orders, are of fundamental importance in analyzing the properties of C. For example, one can use them to construct projective embeddings for moduli spaces of curves. Moreover, they form an important invariant of a curve which is of particular use for the study of automorphisms. In [ ], the authors studied the geomtric classifications of the Weierstrass points of ordre on smooth projective plane septic curves but this classification was not complete. The goal of this paper is to find all the candidates for the 1-Weierstrasss points on smooth projective plane septic curves and to investigate the geometry of such points. The paper contains a variety of examples that illustrate and enrich the subject.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Algebra and applications.

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EXTENSIONS OF VON NEUMANN LOCAL RINGS

SUSAN F. EL-DEKEN , A. AGEEB

Department of Mathematics, Faculty of Science Helwan University, Ain Helwan, 11790, Helwan, Cairo, Egypt

Department of Mathematics, Faculty of Science Al-Azhar University, Nasr City, 11884, Cairo, Egypt

ABSTRACT

This paper introduces an extension of von Neumann local rings (called
EVNL-ring). Among other results, we show that Zn is an EVNL-ring for
all integers n > 1; the direct product of EVNL-rings is an EVNL-ring
and the class of EVNL-rings coincides with the class of C-rings. Also, we
study the case when a formal power series ring is an EVNL-ring.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Algebra and applications.

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An algorithm for the shortest distance path for a graph

H. El- zohny , Afaf Abd El kadr , Z. Mohammed

Al Azhar university

Al Azhar university

Al Azhar university

ABSTRACT

In this article we determine the shortest distance path algorithm between any two distinct vertices for a given graph.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Algebra and applications.

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Rigid rings with involution

Usama A. Aburawash , Bsmaa M. ELgamudi , Muna E. AbdUlhafed

Faculty of Science-Alexandria University

Faculty of Science-Alexandria University

Faculty of Science-Alexandria University

ABSTRACT

Working in the category of rings with involution, we introduce the property of *-rigid and α-*-rigid for *-rings. These new *-rings generalize that of rigid and α-rigid *-rings, respectively. We show also that α-rigid *-rings are α-*-rigid, α-*-reversible and α-*-Armendariz *-rings. Moreover, we give sufficient conditions for α-*-rigid, α-*-reversible and α-*-Armendariz *-rings to be α-rigid. Furthermore, We show that the properties of *-rigid, α-*-rigid, α-*-reversible and α-*-Armendariz are extended to its polynomial *-ring R[x], Laurent polynomial *-ring R[x, x-1], localization (S-1)R of R to S, Ore *-ring Q and Dorroh extension D(R,Z). Finally, we show that if a *-ring R is α-*-Armendariz then the skew polynomial R[x,α] is *-Baer (*-reversible) if and only if R is so.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Algebra and applications.

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Usama's Method for solving linear systems of algebraic equations.

Usama Wadie Aziz Mousa

an engineer of computer and automatic control-faculty of engineering ,Ain_shams university.

ABSTRACT

This document gives My new method for solving linear systems of algebraic equations. I gave the name Usama's method for My Method where I introduced it in the last conference (ICMTD 2015). Usama's method contains equations and rules. Usama's method is more easy than Cramer's rule, where it produces an explicit formula for the solution ,but with less arithmatic operations. and also Usama's method is more easy than Gaussian elimination for producing the solution for the unique solution's linear systems, but without much division operations,where there is only one division operation.