Neda Nedaei, Jafar A'zami, Abolfazl Tehranian: Properties of Cohen-Macaulay modules and extension functors, 231-241

Abstract:

Let $(R,{\mathfrak{m}})$ be a commutative Noetherian local ring with identity. In this paper we investigate the existence of Cohen-Macaulay modules with special annihilators applying the finite filtration of submodules of finitely generated modules. As an application, we deduce several consequences concerning the associated primes of the quotient rings of the ${\mathfrak{m}}$-adic completion of $R$. Also, we shall prove some results concerning the vanishing of extension functors.

Key Words: Associated prime ideal, Cohen-Macaulay module, extension functor, Noetherian local ring.

2010 Mathematics Subject Classification: Primary 13D45; Secondary 14B15.

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