Professor Rashid Abu-Dawwas serves as a Full Professor in the Department of Mathematics and Natural Sciences at Prince Mohammad Bin Fahd University (PMU) in Al Khobar, Saudi Arabia. He works primarily abstract algebra, with a primary focus on graded ring theory and ideal theory. He is particularly interested in developing and studying generalizations of classical ideals within both commutative and non-commutative graded rings, including various prime-like structures such as graded prime ideals, 2-absorbing ideals, and their refinements.
A central theme of his work is understanding how these generalized ideals interact with the structural properties of graded rings and modules. In particular, he investigates their behavior under algebraic constructions such as quotient rings, homomorphisms, and idealizations. These approaches provide deeper insight into the internal structure of graded algebraic systems.
More recently, he has undertaken a detailed and systematic study of a norm function over Z_2-graded rings. This norm function serves as a powerful tool in analyzing the structure of graded rings and in defining new classes of ideals. In particular, he has explored how properties of N(x), such as multiplicativity and idempotency conditions, an be used to characterize novel ideal-theoretic concepts (e.g., N-prime, N-absorbing, and related classes). This perspective provides a unifying framework that connects graded structures with functional identities, leading to new results and deeper structural understanding.
Abu-Dawwas is committed to nurturing the next generation of mathematicians who will contribute meaningfully to the advancement of science in Saudi Arabia and the broader region.
A Sample of Recent Articles:
\item A. Melhem, R. Abu-Dawwas and A. Albalasmeh, On $2$-$\mathcal{N}$-prime ideals over commutative $\mathbb{Z}_2$-graded ring, Journal of Discrete Mathematical Sciences and Cryptography, 29 (3) (2026), 1335-1346.
\item R. Abu-Dawwas and A. Al-Jarrah, $\mathcal{N}$-$r$-ideals and semi $\mathcal{N}$-$r$-ideals of commutative $\mathbb{Z}_2$-graded rings, Boletim da Sociedade Paranaense de Matematica, 44 (6) (2026), 1-9.
\item R. Abu-Dawwas and Q. Jarrah, On graded $\alpha$-prime ideals, accepted in the Palestine Journal of Mathematics, 2025, to appear.
\item R. Abu-Dawwas and E. Al-ali, Strongly Semi $r$-Ideals and Graded Strongly $r$-Ideals, accepted in the Moroccan Journal of Algebra and Geometry with Applications, 2025, to appear.
\item A. S. Alshehry, R. Abu-Dawwas and R. Abudalo, Graded 1-Absorbing Prime Ideals over Non-Commutative Graded Rings, Axioms, 14 (5) (2025), https://doi.org/10.3390/axioms14050365.
\item A. Melhem, R. Abu-Dawwas and R. Ghozlan, Graded $S$-$r$-Ideals, Journal of Discrete Mathematical Sciences and Cryptography, 28 (1) (2025), 267-279, https://doi.org/10.47974/JDMSC-2200.
\item A. S. Alshehry and R. Abu-Dawwas, The Norm Function for Commutative $ \mathbb{Z}_{2}$-Graded Rings, Axioms, 13 (12) (2024), 879; https://doi.org/10.3390/axioms13120879.
\item J. M. Habeb and R. Abu-Dawwas, Graded Classical Weakly Prime Submodules Over Non-Commutative Graded Rings, Tatra Mountains Mathematical Publications, 87 (2024), 85-104.
\item A. Melhem, R. Abu-Dawwas and D. Alghazo, Graded $2r$-Ideals, Results in Nonlinear Analysis, 7 (4) (2024), 64-69.
\item T. Alraqad, H. Saber and R. Abu-Dawwas, EM-Graded Rings, Journal of Mathematics, 2024, https://doi.org/10.1155/jom/6634147.
\item A. S. Alshehry, R. Abu-Dawwas and B. Hawary, Graded weakly strongly quasi-primary ideals over commutative graded rings, Mathematics, 12 (18) (2024), 2857; \\https://doi.org/10.3390/math12182857.
\item R. Abu-Dawwas, A. Assarrar, J. M. Habeb and N. Mahdou, On graded $1$-absorbing $\delta$-primary ideals, Proyecciones Journal of Mathematics, 43 (3) (2024), 571-586.
\item M. Refai, R. Abu-Dawwas, U. Tekir, S. Koc, R. Awawdeh and E. Yildiz, On graded $\phi$-$1$-absorbing prime ideals, Proceedings of the Jangjeon Mathematical Society, 27 (2) (2024), 205-217.
\item A. S. Alshehry, A. AL-Jarrah, R. Abu-Dawwas and A. AL-Kateeb, On rings with involution and inner rings, Results in Nonlinear Analysis, 7 (2) (2024), 79-88.
\item A. S. Alshehry, R. Abu-Dawwas and Muhsen Al-Bashayreh, On properties of graded rings with respect to group homomorphisms, International Journal of Mathematics and Mathematical Sciences, 3803873, (2023), https://doi.org/10.1155/2023/3803873.
\item A. S. Alshehry, R. Abu-Dawwas and Majd Al-Rashdan, Some notes on graded weakly $1$-absorbing primary ideals, Demonstratio Mathematica, 56 (1) (2023), 20230111, https://doi.org/10.1515/dema-2023-0111.
\item M. Bataineh and R. Abu-Dawwas, Graded weakly $1$-absorbing primary ideals, Demonstratio Mathematica, 56 (1) (2023), 20220214, https://doi.org/10.1515/dema-2022-0214.
\item J. Shtayat, R. Abu-Dawwas and G. Bani Issa, Graded almost prime ideals over non-commutative graded rings, Palestine Journal of Mathematics, 12 (3) (2023), 294-300.
\item M. Bataineh and R. Abu-Dawwas, On graded 2-absorbing coprimary submodules, Missouri Journal of Mathematical Sciences, 34 (2) (2022), 174-183.
\item M. Refai and R. Abu-Dawwas, On properties of graded rings and graded modules, Proyecciones Journal of Mathematics, 41 (6) (2022), 1413-1437.
\item R. Abdullah, R. Abu-Dawwas, S. Koc, U. Tekir and E. Yildiz, On graded strongly quasi primary ideals, Moroccan Journal of Algebra and Geometry with Applications, 1 (2) (2022), 409-417.
