1. Parween O. Ali, S. S. Essa (2025). A graph associated with tri-potent elements of commutative ring, Gulf Journal of Mathematics 20(1), 405-413.
2. Essa, S. S., Mohammad, H. Q. (2024). On The Structure of a k-Annihilating Ideal Hypergraph of Commutative Rings, Communications in Mathematics and Application, 15(1): 55-67.
3. Essa, S. S., Mohammad, H. Q. (2023). On The Structure of a k-Annihilating Ideal Hypergraph of Commutative Rings, Comm. Korean Math. Soc., 38(1): 55-67.
4. N. Ibrahim and S. Essa (2020). Journal of Mathematics and Statistics Research 2(2), p. 1–4,.
5. Shuker, N. H., Basheer, D. A., Esa, Sh. S., (2018),"On -Regular Rings and Flatness", Qalaai Zanist Sci. J., Vol.3, No.1, pp.1-10.
6. Esa, Sh. S., Faris, H. S., (2017),"On -clean Ring", Sci. J. Zakho Univ., Vol.5, No.3, pp.285-287.
7. Esa, Sh. S., (2015), "On -VNL-rings", J. Duhok Univ. (Pure and Eng. Sciences), Vol.18, No.1, pp.93-96.

My research interests lie in the broad area of Pure Mathematics, with a particular focus on Algebra and its deep structural aspects. I am especially interested in Ring Theory, where I study algebraic properties that govern the behavior of elements and ideals within various classes of rings. A significant part of my work explores the interplay between algebra and graph theory, specifically through Graph Algebra and Algebraic Combinatorics, where algebraic structures are used to model, analyze, and classify combinatorial objects. This interdisciplinary perspective allows me to investigate new graph constructions—such as idempotent and tri-potent graphs of rings, also zero divisor and unit graph of rings and understand how algebraic properties influence their combinatorial behavior.

My teaching experience encompasses key areas of undergraduate mathematics, including Group Theory and Ring Theory for third-year students, Linear Algebra for second-year students, and Foundations of Mathematics I and II for first-year cohorts. Through these courses, I have guided students from introductory logical reasoning to advanced abstract structures, emphasizing clear explanation, rigorous proof techniques, and critical thinking. My approach focuses on building a strong conceptual foundation while encouraging independent problem-solving, ensuring that students develop the analytical skills essential for success in higher-level mathematics.

My supervision of undergraduate projects and postgraduate theses in Mathematics has centered on guiding students through key areas such as ring theory, group theory, number theory and graph theory, especially; algebraic graph theory. I have supported students in developing clear mathematical reasoning, formulating research questions, and presenting their work with precision. At both levels, my mentorship emphasized analytical thinking, engagement with mathematical literature, and the ability to construct rigorous proofs.

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