Cohen-Macaulay Ring

A Cohen-Macaulay ring is a type of mathematical structure in algebra that exhibits a high level of symmetry and optimal conditions related to its dimensions and regularity. In essence, it has a well-behaved hierarchy of relationships between its elements, allowing for efficient analysis of geometric and algebraic properties. These rings are important because they often simplify complex calculations and lead to a deeper understanding of the geometric objects they model, making them a central concept in commutative algebra and algebraic geometry.