10 May، 2022
Discussion of a doctoral thesis entitled: Idempotent Divisor Graph of Commutative Rings
Discussion of a doctoral thesis in the Faculty of Computer Science and Mathematics – Department of Mathematics entitled:
Idempotent Divisor Graph of Commutative RingsA doctoral thesis was discussed in the discussion hall of the Faculty of Computer Science and Mathematics at the University of Mosul on Monday 9-5-2022, by the student Muhammad Nofal Othman Majid, under the supervision of Prof. Nizar Hamdoun Shukr and Prof. Hossam Qassem Muhammad.
The study dealt with the statement of the denominators of commutative rings by linking two basic theories in mathematics, namely the theories of rings and the statement, in order to identify the properties of rings through the concepts of statement theory.
The study touched on finding new properties for this statement, for example, during which it was proven that this statement is free of edge-block graphs, and the conditions that must be met in the loop were determined so that the statement is free of block itself graphThe study aims to clarify the denominators of the planar neutral element, as it has been proven that the chromatic number is equal to the clique number for this statement and for any commutative ring, in addition to finding the chromatic number, the number of the league, and the color number for the regions chromatic number of this planar statement and for any commutative ring.
On the practical side, the substitutional ring (after finding the denominators of the neutral element for it) was transformed into an artistic optical illusion painting, Op art, and this study is the first of its kind in the world in this field.The discussion committee consisted of Prof. Raeda Daoud Mahmoud – President, and the membership of Prof. Sinan Omar Ibrahim / Tikrit University / College of Education for Girls, Prof. Ammar Siddiq Mahmoud / University of Mosul / College of Education for Pure Sciences, Prof. Dr. Ahmed Muhammad Ali and Prof. Dr. Biman Abbas Rashid / University of Salah al-Din / College of Basic Education, with the membership and supervision of: Prof. Dr. Nizar Hamdoun Shukr and Assistant Professor Dr. Hossam Qassem Mohammed .
