Serre's Criterion is a set of conditions that characterize the property of being Cohen-Macaulay for certain types of rings and modules, primarily focusing on the relationship between flatness and depth. This criterion provides a way to determine whether a module over a local ring is Cohen-Macaulay by examining its flatness and related properties. It connects deeply with concepts such as depth, dimension, and regularity, establishing important links in the study of commutative algebra.
congrats on reading the definition of Serre's Criterion. now let's actually learn it.