Cohen-Macaulay type

The Cohen-Macaulay type is a number that measures how complex the structure of a Cohen-Macaulay ring or algebra is. In algebra, rings are abstract systems that generalize concepts like integers and polynomials. When a ring is Cohen-Macaulay, it has a well-behaved dimension and depth, making it easier to analyze. The Cohen-Macaulay type specifically counts the minimal number of generators needed for a particular ideal associated with the ring—known as the canonical module—reflecting its level of complexity. A lower type indicates a simpler, more "regular" structure, while a higher type signifies greater complexity.