Elementary criteria for irreducibility of $f(X^n)$

TL;DR

This paper presents simple sufficient conditions, based on a generalization of Capelli's theorem, for determining when the polynomial $f(X^n)$ is irreducible over any unique factorization domain.

Contribution

It introduces elementary criteria for irreducibility of $f(X^n)$, extending Capelli's theorem to a broader algebraic setting.

Findings

Provides straightforward irreducibility criteria for polynomials of the form $f(X^n)$

Generalizes Capelli's theorem to arbitrary UFDs

Facilitates easier verification of polynomial irreducibility

Abstract

Very simple sufficient conditions for the irreducibility of $f(X^n)$ over an arbitrary unique factorization domain $Z$ are established via a generalization of a well known theorem of A. Capelli.