Galois Group Correspondence On Extension Fields Over Q

  • Novita Dahoklory Pattimura University
  • Henry W. M. Patty Pattimura University
Keywords: Extension fields, Galois extension, Galois correspondence

Abstract

Let  be an extension field where  denotes dimension of  as a vector space over . Let  be the group of all automorphism of  that fixes  where the order of  is denoted by . Particularly, an extension field is called a Galois extension if . Moreover, we will give some properties of an extension field  which is a Galois extension. Using the properties of Galois extension, we will show that there is an one-one correspondence between the set of all intermediate fields in  and the set of all subgroups in . Furthermore, we will give some examples of Galois group correspondence using an extension field over .

 

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References

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Malik, D. S., & Mordeson, J. N. MTH 581-582 Introduction to Abstract Algebra. America, February., 2007.

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Published
2023-04-03
How to Cite
Dahoklory, N., & Patty, H. W. M. (2023). Galois Group Correspondence On Extension Fields Over Q. Pattimura Proceeding: Conference of Science and Technology, 4(1), 17-28. Retrieved from https://ojs3.unpatti.ac.id/index.php/pcst/article/view/8599
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Articles