Chinese Remainder Theorem for Cyclotomic Polynomials in $\mathbf{Z}[X]$

Kamalakshya Mahatab, Kannappan Sampath

By the Chinese remainder theorem, the canonical map \[Ψ_n: R[X]/(X^n-1)\to \oplus_{d|n} R[X]/Φ_d(X)\] is an isomorphism when $R$ is a field whose characteristic does not divide $n$…