ZULFI’S COLLEGE OF SCIENCE
Research Group:
Abstract Algebra and Applications
College of Science in Al-Zulfi
Dr Rabah Kellil
Assistant Prof.
r.kellil@mu.edu;sa
Presentation
The group (3AG) is a research group of the Department of Mathematics at
the College of Science of Majmaah University. The group performs a research
activity in many areas of abstract algebra and its applications in various
domains as coding theory (finite fields), cryptography (finite fields) , abstract
computer science (semirings), genetics (biordered sets), tropical geometry ,
etc…
Outline of Research
Algebra is the language of modern mathematics. When the rules of
addition and multiplication are generalized, their precise definitions lead to the
notions of algebraic structures such as groups, rings, semirings, and fields
which are actually studied in the area of mathematics called abstract algebra.
Algebra is one of the main branches of mathematics, together with geometry,
analysis, topology, combinatory and number theory.
The Department of Mathematics at College of Science in Al-Zulfi of
Majmaah University is performing the research activities in algebraic
structures. The research group of abstract algebra, covers a wide spectrum of
interests, from group theory, semigroup theory, semiring theory, and their
applications in computer science, biology (genetics), coding theory (finite
fields), cryptography (finite fields), and tropical geometry. This research group
is also performing the research activities on algebra in terms of rough set
theory, fuzzy set theory and soft set theory in collaboration with worldwide
famous mathematicians.
Major Research Topics
Groups, semigroups, rings and semirings
General tropical rings and coding theory on rings
Hyperstructures (in particular: Hypergroups, Semihypergroups, Gammasemihypergroups)
Non-associative semigroups and non-associative semihypergroups
Ternary algebraic structures and ternary algebraic hyperstructures
Partial ordering on algebraic structures and algebraic hyperstructures
Ideal theory of subtraction algebras and BCK-algebras
Algebraic structures and algebraic hyperstructures in terms of rough sets,
fuzzy sets and soft sets.
References (recent publications)
-Rabah Kellil, Some Propreties on Morphic Groups. Pure Mathematical Sciences, Vol. 2,
2013, no. 2, 55 – 68. HIKARI Ltd
-Rabah Kellil, External approach of ideals in subtraction algebras. Asian Journal of Current
Engineering and Maths . 2: 2 March – April (2013) 115 – 117.
-Rabah Kellil, Some Aspects of Derivation in Ternary Semirings. International Journal of
Multidisciplinary Sciences and Engineering. Volume 4, Issue 5, June 2013
-Rabah Kellil, Green’s realtions on ternary semigroups. J. Semigroup Theory Appl. 2013,
2013:6
-Rabah Kellil, On inverses of left almost semirings and strong left semirings. Journal of
Mathematical Sciences: Advances and Applications, issue 2014
-F. Yousafzai, N. Yaqoob and A. Zeb, On generalized fuzzy ideals of ordered AGgroupoids, International Journal of Machine Learning and Cybernetics, in press, doi:
10.1007/s13042-014-0305-6.
-M. Khan, Y.B. Jun, M. Gulistan and N. Yaqoob, The generalized version of Jun's cubic
sets in semigroups, Journal of Intelligent and Fuzzy Systems, in press, doi: 10.3233/IFS141377. (ISI Impact Factor 0.936)
-N. Yaqoob, M. Aslam, B. Davvaz and A. Ghareeb, Structures of bipolar fuzzy Γhyperideals in Γ-semihypergroups, Journal of Intelligent and Fuzzy Systems, in press, doi:
10.3233/IFS-141260. (ISI Impact Factor 0.936)
-N. Yaqoob and M. Gulistan, Partially ordered left almost semihypergroups, Journal of the
Egyptian Mathematical Society, in press, doi: 10.1016/j.joems.2014.05.012.
-N. Yaqoob and M. Aslam, Generalized rough approximations in Γ-semihypergroups,
Journal of Intelligent and Fuzzy Systems, in press, doi:) 10.3233/IFS-141214. (ISI Impact
Factor 0.936)
-N. Yaqoob and S. Haq, Generalized Rough Γ-hyperideals in Γ-semihypergroups, Journal
of Applied Mathematics, Article ID 658252 (2014) 6 pages. (ISI Impact Factor 0.72
Mr Naveed Yaqoob
Lecturer
na.yaqoob@mu.edu.sa
Objectives
Determine some particular properties of morphic groups.
As an application of the semigroups in computer science; we study the
semigroup actions since they are closely related to automata with as a set
models; the state of the automaton and the action models transformations of
that state in response to inputs. The principal references are:
Mati Kilp, Ulrich Knauer, Alexander V. Mikhalev (2000), Monoids, Acts
and Categories: with Applications to Wreath Products and Graphs,
Expositions in Mathematics29, Walter de Gruyter, Berlin, ISBN 978-3-11015248-7.
Rudolf Lidl and Günter Pilz, Applied Abstract Algebra (1998),
Springer, ISBN 978-0-387-98290-8
Since the works of Kleene and after those of Samuel Eilenberg, Semirings
can be applied in automata theory and formal language, where a
comprehensive algebraic theory has been constructed and published in four
volumes on Automata, Languages, and Machines. The basic algebraic
structures used in these books, and the publications of many other
researchers, were semirings. Our research is concerned with study some
new properties and to study which properties can be obtained in the ternary
semirings.
One of our recent axe of our interest is the study of tropical geometry and
our idea is to define general tropical semiring and extract the properties in
view of those known in the case of the tropical semifield (R,max,+).
Our aim is to study the properties of fuzzy sets, rough sets and soft sets in
algebraic (hyper)structures.
Submitted Papers
1. Thai Journal of Mathematics
Rabah Kellil
Idempotents, band and Green’s relations on ternary semigroups
Oct 25, 2013. In review
2. Indian Journal of Pure and Applied Mathematics
Rabah Kellil
Idempotent and Inverse Elements in Strong ternary semirings
Sep 06, 2014. In Review
3. Southeast Asian Bulletin of Mathematics
Rabah Kellil and Ferdaous Kellil
Intra-regular ordred ternary ∗-semigroup
None
RABAH KELLIL
Oct 17, 2014. In Review
4. Journal of Intelligent and Fuzzy Systems
Rabah Kellil and Ferdaous Kellil
A Brief introduction to topological Hypergroups
None
RABAH KELLIL
Mar 8, 2015. In review
5. Italian Journal of Pure and Applied Mathematics
Rabah Kellil
Hypergroups and Fuzzy sets associated modulo a subgroup
Apr 5, 2015. In Review
6. Afrika Matematika
Madad Khan, Muhammad Gulistan, Naveed Yaqoob and Fawad Hussain
General cubic hyperideals of LA-semihypergroups
In Review
7. Songklanakarin Journal of Science and Technology
Madad Khan, Bijan Davvaz, Naveed Yaqoob and Muhammad Gulistan
On (∈,∈∨qk)-intuitionistic (fuzzy ideals, fuzzy soft ideals) of subtraction algebras
In Review