Properties Of Weak CM Rings

In this paper,we mainly study the properties of weak CM rings.It is a special class of Noetherian commutative rings,including Cohen-Macaulay rings,excellent rings and generalized Cohen-Macaulay rings,which can be characterized by local cohomology modules.We will prove that if i? is a weak CM ring,then every localized ring of R,every finitely generated algebra of R,and the /—adic complete ring of R with respect to any ideal I of R are still weak CM rings,and the Cohen-Macaulay locus of i? is a open set of Spec R.Moreover,a sufficient and necessary condition for a finitely generated module on a weak CM ring having a uniform local cohomological annihilator is given in the paper.