College of Education for Pure Science

Master Thesis Viva in the College of Education for Pure Science entitled ” Hopf-Galois Structures On Non-normal Extensions Of Degree “The College of Education for Pure Science, University of Mosul, has done the Master Thesis Viva entitled ” Hopf-Galois Structures On Non-normal Extensions Of Degree “,On Tuesday, October 11, 2022, the College staff including the respected Dean of the College, Assistant Professor Dr. Qais Ismail Ibrahim, the Honorable Scientific Associate and Administrative Associate, the Honorable Head of the Department of Mathematics, and a number of the college’s teachers were attended the viva. This study, presented by the Master student Baraa Muthana Jamal Jasim in the Department of Mathematics, studies Hopf-Galois structures on separable (non-normal) field extensions of square-free degree , where is Sophie Germain prime, is the corresponding Safe prime and are square-free primes.Byott and Lyons (Byott & Martin-Lyons, 2022) haves studied Hopf-Galois structures on non-normal extensions of degree . They posit a problem of investigating wheather the same behaviour occurs for more general square-free degrees.Also it investigated in details the cyclic and non-abelian cases of Hopf-Galois structures on non-normal extensions of degree . We determine the permutation groups , then we enumerate the Hopf-Galois structures for each . There are fifty-four (four) for which the field extensions admit Hopf-Galois structures in cyclic (non-abelian) case respectively.The Viva committee was chaired by Prof. Dr. Ammar Seddiq Mahmood/ University of Mosul, College of Education for Pure Science and the membership of Prof. Dr. Sinan Omar Ibrahim / University of Tikrit /College of Education, Asst. Prof. Zubaida Muhammad Ibrahim , University of Mosul, College of Computer Science and Mathematics, and under the supervision and membership of Lecturer Dr. Ali Abdulqader Bilal, University of Mosul, College of Education for Pure Sciences.