But if "R" is a Noetherian local ring and the elements "r""i" are in the maximal ideal, or if "R" is a graded ring and the "r""i" are homogeneous of positive degree, then any permutation of a regular sequence is a regular sequence. Let "R" be a Noetherian ring, "I" an ideal in "R", and "M" a finitely generated "R"-module. The depth of "I" on "M", written depth"R"("I", "M") or just depth("I", "M"), is the supremum of the lengths of all "M"-regular sequences of elements of "I". When "R" is a Noetherian local ring and "M" is a finitely generated "R"-module, the depth of "M", written depth"R"("M") or just depth("M"), means depth"R"("m", "M"); that is, it is the supremum of the lengths of all "M"-regular sequences in the maximal ideal "m" of "R". In particular, the depth of a Noetherian local ring "R" means the depth of "R" as a "R"-module. That is, the depth of "R" is the maximum length of a regular sequence in the maximal ideal. For a Noetherian local ring "R", the depth of the zero module is ∞, whereas the depth of a nonzero finitely generated "R"-module "M" is at most the Krull dimension of "M" (also called the dimension of the support of "M"). An important case is when the depth of a local ring "R" is equal to its Krull dimension: "R" is then said to be Cohen-Macaulay. The three examples shown are all Cohen-Macaulay rings. Similarly, a finitely generated "R"-module "M" is said to be Cohen-Macaulay if its depth equals its dimension. A simple non-example of a regular sequence is given by the sequence formula_3 of elements in formula_4 since has a non-trivial kernel given by the ideal formula_6 . Similar examples can be found by looking at minimal generators for the ideals generated from reducible schemes with multiple components and taking the subscheme of a component, but fattened. In the special case where "R" is the polynomial ring "k"["r"1, ..., "r""d"], this gives a resolution of "k" as an "R"-module.   is isomorphic to the polynomial ring ("R"/"I")["x"1, ..., "x""d"].