Fundamental Properties of the Galois Correspondence
Ayinde S. Olukayode and Oyekan E. Abiodun
DOI : 10.3844/jmssp.2008.245.249
Journal of Mathematics and Statistics
Volume 4, Issue 4
Problem Statement: Let K is the splitting field of a polynomial f(x) over a field F and αn be the roots of f in K. Let G be embedded as a subgroup of the symmetric group ς. We determined the Galois group G, and the subgroup. Approach: computed some auxiliary polynomials that had roots in K, where the permutation of a set was considered distinct. The Galois Theory was deduced using the primitive element and Splitting theorems. Results: The Galois extension K/L to identity L and its Galois group is a subgroup of G. which was referred to as the main theorem which we proved. Conclusion: Hence the findings suggest the need for computing more auxiliary polynomials that have roots.
© 2008 Ayinde S. Olukayode and Oyekan E. Abiodun. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.