Finite fields occupy an important and elementary part of number theory, but I can’t seem to find good literature on this topic. Can anyone help me?
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Hachenberger, Jungnickel, "Topics in Galois Fields" – Kenta S Mar 28 '21 at 15:20
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1Does this answer your question? Good books for a high schooler self-studying Abstract Algebra? – vitamin d Mar 28 '21 at 15:29
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2It really depends on your level of studies and focus of interest. Your Question would be improved by adding such context. For example, a reference that explores polynomial irreducibility over finite fields using computer algebra software might be useful if you have sufficient background and interest. – hardmath Mar 28 '21 at 15:40
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Any comprehensive graduate abstract algebra textbook. Hungerford, Dummit & Foote, etc. – D_S Mar 28 '21 at 16:52
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See https://www.cambridge.org/core/books/finite-fields/75BDAA74ABAE713196E718392B9E5E72 – lhf Mar 28 '21 at 17:15
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I found Introduction to finite fields and their applications by R. Lidl and H. Niederreiter very helpful.
Update: This book (or better a successor version) is also available as volume 20 in the Cambridge series Encyclopedia of Mathematics and its Applications indicating its high quality status.
It is titled Finite Fields. The first six chapters are essentially the same. Chapter V has been extended by three sections: Jabobi Sums, Character Sums with Polynomial Arguments and Further Results on Character Sums. The final four sections have been extended and somewhat rearranged.
Markus Scheuer
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Fried, Michael D.; Jarden, Moshe, Field arithmetic, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge 11. Berlin: Springer (ISBN 3-540-22811-X/hbk). xxii, 780 p. (2005). ZBL1055.12003.
Is the book many experts use.
Igor Rivin
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