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An Introduction to the Theory of Field Extensions
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作者 Saviour Chibeti Iness Kyapwanyama +1 位作者 Henry M. Phiri Jeromy Kalunga 《Advances in Pure Mathematics》 2023年第2期103-132,共30页
This paper unfolds and reviews the theory of abstract algebra, field extensions and discusses various kinds of field extensions. Field extensions are said to be algebraic or transcendental. We pay much attention to al... This paper unfolds and reviews the theory of abstract algebra, field extensions and discusses various kinds of field extensions. Field extensions are said to be algebraic or transcendental. We pay much attention to algebraic extensions. Finally, we construct finite extensions of Q and finite extensions of the function field over finite field F<sub>p </sub>using the notion of field completion, analogous to field extensions. With the study of field extensions, considering any polynomial with coefficients in the field, we can find the roots of the polynomial, and with the notion of algebraically closed fields, we have one field, F, where we can find the roots of any polynomial with coefficients in F. 展开更多
关键词 fields Extension fields Algebraic and Transcendental Extension Algebraic Closure Algebraically Closed field Absolute Value COMPLETION P-Adic field and field of formal laurent series
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