Fundamental Properties of the Galois Correspondence | Science Publications

Journal of Mathematics and Statistics

Ayinde S. Olukayode¹  Oyekan E. Abiodun¹ 

关键词: Splitting fields;    symmetric group;    galois group and theory;    resolvents;   

DOI  :  10.3844/jmssp.2008.245.249

学科分类：社会科学、人文和艺术（综合）

来源: Science Publications

【 摘 要 】

Problem Statement: Let K is the splitting field of a polynomial f(x) over a field F and α_n 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.

【 授权许可】

Unknown