A Note on Abelian Monogenic Trinomials

An abelian monogenic polynomial f ( x ) ∈ Z [ x ] f(x)∈ Z[x] f left parenthesis x right parenthesis element of double struck upper Z left bracket x right bracket is a monic polynomial of degree N ≥ 2 N≥ 2 upper N greater than or equals 2 that is irreducible over Q Q double struck upper Q , such that the Galois group of f ( x ) $f(x)$ f left parenthesis x right parenthesis over Q Q double struck upper Q is abelian, and { 1 , θ , θ 2 , … , θ N − 1 } \1,θ ,θ ²,… ,θ N-1\ StartSet 1 comma theta comma theta squared comma ellipsis comma theta Superscript upper N minus 1 Baseline EndSet is a basis for the ring of integers of Q ( θ ) Q(θ ) <jats:inline-graphic xmlns:xlink="http: