CURRICULUM VITAE Hani Abdel-Aziz Khashan Professor Department of Mathematics Al Al-Bayt University P.O. Box 130095 Al-Mafraq-Jordan e-mail: hakhashan@aabu.edu.jo Mobile: 00962795005319 ACADEMIC QUALIFICATIONS PhD (2003), Mathematics, University of Jordan, Jordan. MS (1994), Mathematics, Yarmouk University, Jordan. BS (1991), Mathematics, Yarmouk University, Jordan. EXPERIENCE Vice Dean of the Deanship of Graduate Studies: September 2017-Present, Deanship of Graduate Studies, Al al-bayt University. Vice Dean of the Faculty of Science: September 2013- September 2015, Faculty of Science, Al al-bayt University, Jordan. Head of the Department of Mathematics: September 2012-September 2013, Department of Mathematics, Al al-bayt University, Jordan. Professor: March 2018- Present, Department of Mathematics, Al al-bayt University, Jordan. Associate Professor: May 2010-Present, Department of Mathematics, Al Al-Bayt University, Jordan. Associate Professor: September 2010-September 2011, Department of Mathematics, University of Jordan, Jordan.
Assistant Professor: Feb 2004-May 2010, Department of Mathematics, Al Al-Bayt University, Jordan. Assistant Professor: Sep 2003-Feb 2004, Department of Mathematics, Applied Science University, Jordan. Visiting Professor: Sep 2005-January 2006, Department of Mathematics, United Arab Emirates University, United Arab Emirates. RESEARCH INTERESTS * Commutative rings with identities - Q-rings and almost Q-rings. - Generalizations of prime ideals and submodules. - Graded rings and modules. - Clean rings and their generalizations. * Application of groups and rings in numerical analysis - Solving systems of polynomials - Exploiting permutation symmetry in solving linear systems. PUBLICATIONS 1. Hani A. Khashan and H. Alezeh, Conditions under which R(x ) and R x are almost Q- rings. Archivum Mathmaticum (Brno), vol 43 (2007), pp. 231-236. 2. M.Syam, H. Khashan and Q. Al-Mudallal, Nonlinear eigenvalue problems with symmetry. Chaos, Solitons & Fractals, vol 35 (5), (2008), pp. 931-941. 3.Hani A. Khashan, Some properties of gr-multiplication ideals. Turkish Journal of Mathematics, vol 32 (2008), pp. 1-12. 4. Hani A. Khashan, Graded rings in which every graded ideal is a product of grprimary ideals. International Journal of Algebra, vol 2 (16), (2008), pp.779-788. 5. A. Jaber, M. Bataineh and Hani A. Khashan, Almost Graded prime ideals. Journal of Mathematics and Statistics, vol 4 (3), (2008), pp.166-171. 6. Hani A. Khashan and M. Syam, QR-algebraic method for approximating zeros of system of polynomials. International Journal of Computer Mathematics, vol 88 (1) (2011), pp. 110-120. 7. Hani A. Khashan, A. Jaber and M. Bataineh, Graded rings in which every proper graded ideal is almost gr-prime, Journal of Mathematical Sciences, Advances and Applications vol 3 (1), (2009), pp. 41-58. 8. Hani A. Khashan, On Almost Prime Submodules, Acta Mathematica Scientia, vol 32 (2), (2012), pp. 645-651.
9. Hani A. Khashan and W. Burhan, Cleanness of Overrings of Polynomial Rings, Egyptian journal of Mathematics, vol 24 (1), (2016), pp. 1-4. 10. Hani A. Khashan and Ali H. Handam, g(x)-nil clean ring. Scientiae Mathematicae Japonicae 79, No.2, (2016) 11. Hani A. Khashan, NR-clean rings, Vietnam J. Math. 44 (4), (2016), 749-759. 12. Ali H. Handam and Hani A. Khashan, Rings in which elements are the sum of a nilpotent and a root of a fixed polynomial that commute. Open Math.15 (2017), 420 426. 13. Hani A. Khashan, On (weakly) precious rings associated to central polynomials, Bulletin of Parana s Mathematical Society 36 (2), (2018): 245 256. 14. Hani A. Khashan and Ali H. Handam, On Weakly g(x)-nil clean ring, International Journal of Pure and Applied Mathematics 114 (2), (2017). 15. Hani A. Khashan and Ali H. Handam, (Weakly) n-nil Cleanness of The Ring Zm, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 67(2), (2018), 29-37. 16. Lumnije, K. Shehu and Hani A. Khashan, Extensions of polygroups by polygroups via quotient polygroups, Accepted in Filomat, preprint. TEACHING EFFECTIVENESS Al al-bayt University: Graduate Level: Math 742: Rings Theory Math 741: Groups Theory Math 702: Methods of Modern Scientific Research in Mathematics Undergraduate Level: Math 101: Calculus I Math 102: Calculus II Math 241: Linear Algebra I Math 251: Logic and Set Theory Math 271: Finance Mathematics Math 301: Real Analysis I Math 342: Abstract algebra I (Groups Theory) Math 343: Graphs Theory Math 344: Number Theory Math 421: Numerical Analysis II Math 441: Linear Algebra I Math 442: Abstract Algebra II (Rings Theory) Math 401: Real Analysis II Math 303: Complex Analysis I
University of Jordan: Math 0301101: Calculus I Math 0301102: Calculus II Math 0301241: Linear Algebra I Math 0301342: Number Theory Math 0301371: Mathematical Programming United Arab Emirates University: Math 321: Linear Programming Math 140: Linear Algebra (1) Math 340: Abstract Algebra Math 370: Math & Eng. Appl. (4) Applied Science University: Math 342: Groups Theory Math 251: Logic and Set Theory Math 101: Calculus I Math 241: Linear Algebra I INTERNATIONAL CONFERENCES (TALKS) Interdisciplinary Mathematical & Statistical Techniques (Shanghai 2007), China. Title: Locally Q-rings. The Fourth International Conference on Mathematical Sciences ICM 2012 (Al-Ain, United Arab University). Title: Conditions under which R(x) and R<x> are (almost) clean rings. International Conference On Algebra in Honour of Leonid BOKUT and Surender K. JAIN (ICA, 2016) (Balikesir-Turkey). Title: On n-nil clean rings. 3rd International Conference on Computational Mathematics and Engineering Sciences CMES2018 (CYPRUS). Title: A New Generalization of the Wreath Product of Polygroups. MASTER'S THESIS SUPERVISION Supervisor of MS thesis titled (Exploiting Permutation Representations in Solving Systems of Linear Equations) Supervisor of MS thesis titled (A study On weakly prime submodules) Supervisor of MS thesis titled ( On commutative rings with domain-type properties). Supervisor of MS thesis titled ( A study on some generalizations of commutative clean rings). Supervisor of MS thesis titled ( Generalizations of von Neumann regular elements in commutative rings).
Supervisor of MS thesis titled ( Cleanness of overrings of polynomials rings) Supervisor of MS thesis titled (Extensions of Polygroups by Polygroups) Supervisor of MS thesis titled (Generalizations of n-ideals in Commutative Rings) Other Scholar Activities An external examiner for more than 20 MS thesis in Jordan Universities. Evaluation committee for more than 40 MS thesis in Al al-bayt University. An editorial board for the radical Journal of Mathematics A reviewer for the radical Journal of Mathematics. A reviewer for the Acta Mathematica Scienetia Journal. A reviewer for the Jordan Journal of Mathematics and statistics. Academic adviser for many students. An organizing committee in the First International Science Conference (ISC). A member in several departmental and college committeessuch as: - Scientific research committee. - Graduate affairs committee. - Social committee. - Exams committee. - Teaching schedule committee. - Library committee. - Recruitment and promotion committee. - Scientific day committee. - Revising Curriculum Committee. Research Statement: I am interested in certain generalizations of prime ideals in commutative rings and prime submodules of unitary modules. Examples of such generalizations are weakly prime ideals (submodules), n-almost prime ideals (submodules) and n-absorbing ideals (submodules). Indeed, I have introduced and studied the concept of almost prime submodules in 2012. I am continuously exploring new generalizations of such concepts by considering primary ideas and submodules. I am primarily interested in graded rings and modules. In some of my research papers, I defined and studied almost graded prime ideals and many properties of graded multiplication ideals. In my research endeavors, for some applications of groups and rings theory, I have introduced and studied a method for solving a system of linear equations numerically by exploiting permutation symmetry. I have also introduced QRalgebraic method for approximating zeros of system of polynomials. I am striving for the development of such methods with support of some experts in numerical analysis.
I have great interest in the concepts of clean and nil-clean associative rings with identity. Those classes of rings have been introduced and studied extensively during the last 4 decades. I am continuously focusing on generalizations of such rings. I have defined and studied the classes of NR-clean, g(x)-nil clean, weakly g(x)- nil clean and g(x)-precious rings. The theory of algebraic hyperstructures which is a generalization of ordinary algebraic structures has been introduced by Marty(1934). Since then, many researchers have studied the theory of hyperstructures and developed it. Recently, I have started a research concerning hypergroups and hyperrings. Among three kinds of hyperrings, I have focused on a Krasner hyperrings where the addition is a hyper operation and the multiplication is the ordinary operation. What I am looking forward to is studying some applications of this theory in other fields such as geometry, graphs and hypergraphs. Research Keywords: Clean Rings Nil-clean Rings g(x)-nil Clean Rings g(x)-precious Rings Almost Q-Rings Almost Prime Ideals Almost Graded Prime Ideals Almost Prime Submodules Permutation Symmetry NR-clean Rings The Rings R(X) and R> x < Hyper structure