Questions tagged [cohen-macaulay]

A ring is called Cohen-Macaulay if its depth is equal to its dimension. More generally, a commutative ring is called Cohen-Macaulay if is Noetherian and all of its localizations at prime ideals are Cohen-Macaulay. In geometric terms, a scheme is called Cohen-Macaulay if it is locally Noetherian and its local ring at every point is Cohen–Macaulay.

A ring is called Cohen-Macaulay if its depth is equal to its dimension. More generally, a commutative ring is called Cohen-Macaulay if it is Noetherian and all of its localizations at prime ideals are Cohen-Macaulay. In geometric terms, a scheme is called Cohen-Macaulay if it is locally Noetherian and its local ring at every point is Cohen–Macaulay.