ΜΕΜ-227 Field Theory (Εαρινό 2026)

Section outline

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  Course Information

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  Instructor

  Theodoulos Garefalakis

  Office	Γ216
  email	tgaref@uoc.gr

   

  Weekly Schedule

  Lecture	Monday and Friday 11:00-13:00 (Room E204)

   

  Reading Material

  1. J. Rotman, Galois Theory, 2nd ed., Springer
  2. I. Stewart, Galois Theory, 5th ed., CRC Press.
  3. P. Morandi, Field and Galois Theory, Springer.
  4. D.S. Dummit and R.M. Foote, Abstract Algebra, Wiley.

   

  Evaluation

  There will be a midterm exam and a final exam. The final mark is computed as

  $\text{Mark} = \max\{ 0.3\cdot \text{Midterm} + 0.7\cdot \text{Exam}, \text{Exam}\}$

  The mark of the midterm does not count towards other evaluation periods (e.g. September, January examinations).

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• Select section 29 January - 4 February

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  29 January - 4 February

  We reviewed some basic structures and theorems that will be needed throughout the course. In particular, we recalled the notions of ring, domain, field, ideal of a domain, principal ideal domain (PID), prime element and prime ideal, irreducible element and maximal ideal.

  We proved Eisenstein's irreducibility criterion and saw Gauss' Lemma on the irreducibility of polynomials over unique factorization domains and their field of fractions.

  We saw that a field K is a vector space over any subfield F, and defined degree of the extension K/F to be the dimension of K as an F-space. We denote it by $[K : F]$. We saw examples.
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