Monoid ring

A **monoid ring** is an algebraic structure that combines concepts from both ring theory and the theory of monoids. Specifically, it is formed from a monoid \( M \) and a ring \( R \). Here's a more detailed breakdown of what this means: 1. **Monoid**: A monoid is a set \( M \) equipped with a single associative binary operation (let's denote it by \( \cdot \)) and an identity element \( e \).