Polynomial identity ring

A **polynomial identity ring**, often denoted as \( R[x] \), is a specific type of ring formed by polynomials with coefficients from a ring \( R \). Here's a breakdown of the concepts involved: 1. **Polynomial Ring**: Given a ring \( R \), the polynomial ring \( R[x] \) is the set of all polynomials in the variable \( x \) with coefficients in \( R \).