Contents of Report

[Data of Report]

	Abstract	.... 3
1	Introduction	.... 4
2	Description of Finite Extension Fields	.... 5
2.1	Extension Generated by One Element	.... 5
2.2	Extension Generated by Two or More Elements	.... 6
3	Primitive Elements	.... 7
3.1	Preliminary Definitions and Notations	.... 7
3.2	Norms	.... 7
3.3	Finding Primitive Elements From(I)	.... 8
3.4	Finding Primitive Elements From (II)	.... 12
3.5	Construction of Norms and Minimal Polynomials	.... 13
3.6	Representation of a and B by a Primitive Element r	.... 15
3.7	The Case Where B Is Given by FB	.... 16
3.8	Algorithm	.... 18
4	Splitting Fields of Polynomials	.... 21
4.1	Extension of Theorem 3	.... 21
4.2	Finding Primitive Elements of Splitting Fields	.... 22
4.3	Algorithms and Remarks	.... 26
	Acknowledgements	.... 28
	References	.... 28

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