Monoid ring
= Monoid ring
{wiki=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 \\).