PT EN

Fundamental Algebra

Program

Group actions, Sylow theory. Nilpotent and solvable groups. Free groups and presentations. Lie groups and algebraic groups. Groups with operators. Rings and modules. Hermite, Smith and Jordan normal forms for matrices. Wedderburn theory. Linear representations of groups. Polynomial rings and factorization theory. Field extensions. Galois theory. Norms, traces and discriminants. Ideal theory in commutative rings. Rings of integers. Dedekind domains. Algebraic sets and Hilbert's Nullstellensatz.

The program will cover most of the above topics. Depending on the background and interests of the students, some topics may be developed in considerably more depth than others.

 

Research and Events

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Defended Theses

  • Structure, algorithmics and dynamics of endomorphisms for certain classes of groups
      André da Cruz Carvalho (April 2023)
      Pedro V. Silva
  • A point-free study of z-embeddings, more general classes of localic maps, and uniform continuity
      Ana Belén Avilez García (April 2023)
      Jorge Picado
  • Analysis of equations of motion of inextensible strings and networks
      Ayk Telciyan (April 2023)
      Dmitry Vorotnikov
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