A logical approach to abstract algebra

Paper in proceeding, 2005

Recent work in constructive mathematics show that Hilbert's program works for a large part of abstract algebra. Furthermore the arguments we get are not only elementary but also mathematically simpler. We present an example where the simplification was significant enough to suggest an improved version of a classical theorem. For this we use a general method to transform some logically complex first-order formulae in a geometrical form which may be interesting in itself.