In this note we investigate some results which concern the types of local rings. In particular it is shown that if the type of a quasi-unmixed local ring A is less than or equal to depth A + 1, and $\hat{A}_p$ is Cohen-Macaulay for every prime $p\ne...
In this note we investigate some results which concern the types of local rings. In particular it is shown that if the type of a quasi-unmixed local ring A is less than or equal to depth A + 1, and $\hat{A}_p$ is Cohen-Macaulay for every prime $p\neq\hat{m}$, then A is Cohen-Macaulay. (This implies the previously known result: if A satisfies $(S_{n-1})}$, where n is the type of a .ins A, then A is Cohen-Macaulay.)