Satapathy, Purnima (2012) Finite Fields. MSc thesis.
In this report, we revised some important definitions with examples and results of ring theory such as ring homomorphism, Euclidean domain, principal ideal domain, unique factorization domain, polynomial rings, irreducibility criteria etc. Then, we discuss field
theory. In field theory, we study the details of extension of fields, splitting fields, algebraic extensions etc. The most important field of abstract algebra is Galois theory. Here, we prove the fundamental theorem of Galois theory and the application of this result. Lastly, we discuss the structure and applications of finite fields.
|Item Type:||Thesis ( MSc)|
|Uncontrolled Keywords:||Extension of Fields,Splitting Fields,Algebraic Extensions,Normal extension, Galois extension, Finite Fields|
|Subjects:||Mathematics and Statistics > Topology|
|Divisions:||Sciences > Department of Mathematics|
|Deposited By:||PURNIMA SATAPATHY|
|Deposited On:||15 May 2012 11:08|
|Last Modified:||15 May 2012 11:08|
|Supervisor(s):||Tungala, R S|
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