A GALOIS THEORY FOR THE FIELD EXTENSION K((X))/K

Galois Theory for Arbitrary Field Extensions

Quantum Theory on a Galois Field

Systems of free particles in a quantum theory based on a Galois field (GFQT) are discussed in detail. In this approach infinities cannot exist, the cosmological constant problem does not arise and one irreducible representation of the symmetry algebra necessarily describes a particle and its antiparticle simultaneously. As a consequence, well known results of the standard theory (spin-statistic...

Exercises in Field Theory and Galois Theory

1. Algebraic extensions (1) Let F be a finite field with characteristic p. Prove that |F | = p n for some n. (2) Using f (x) = x 2 + x − 1 and g(x) = x 3 − x + 1, construct finite fields containing 4, 8, 9, 27 elements. Write down multiplication tables for the fields with 4 and 9 elements and verify that the multiplicative groups of these fields are cyclic.

Coalgebra-galois Extensions from the Extension Theory Point of View

Coalgebra-Galois extensions generalise Hopf-Galois extensions, which can be viewed as non-commutative torsors. In this paper it is analysed when a coalgebra-Galois extension is a separable, split, or strongly separable extension.

galois extension for a compact quantum group

The aim of this paper is to introduce the quantum analogues of torsors for a compact quantum group and to investigate their relations with representation theory. Let A be a Hopf algebra over a field k. A theorem of Ulbrich asserts that there is an equivalence of categories between neutral fibre functors on the category of finitedimensional A-comodules and A-Galois extensions of k. We give the c...