# Journal of the Ramanujan Mathematical Society

Volume 39, Issue 3, September 2024 pp. 293–305.

Discriminant and integral basis of pure nonic fields

**Authors**:
Anuj Jakhar and Neeraj Sangwan

**Author institution:**Indian Institute of Technology (IIT) Madras, India.

**Summary: **
Let K = Q(θ) be an algebraic number field with θ satisfying an
irreducible polynomial x{9} − a over the field Q of rationals and Z{K} denote
the ring of algebraic integers of K. In this article, we provide the exact
power of each prime which divides the index of the subgroup Z[θ] in
Z{K}. Further, we give a p-integral basis of K for each prime p. These
p-integral bases lead to a construction of an integral basis of K which is
illustrated with examples.

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