Depth (ring theory)

In the context of ring theory, "depth" is a concept that arises in commutative algebra, particularly in the study of modules over rings. Depth provides a measure of the "complexity" of the structure of a module, as well as information about the relationship between the module and its associated ring. More formally, the depth of a module \( M \) over a ring \( R \) can be defined in terms of the associated prime ideals.