Cyclotomic subfields

The main purpose of the talk is to show some recent results on cyclotomic subfields. Considering the totally real subfield of the m-th cyclotimc field, we introduce a class of polynomials that could be considered as cyclotomic polynomials of the second kind. Given a divisor d of phi(m), we determine an intermediate subfield of degree d, identifying explicitly the primitive element. The talk includes a series of illustrative examples and an opportunity to further developing our current work.