Cohomological dimension and relative Cohen-Maculayness

Abstract

Let R be a commutative Noetherian (not necessary local) ring with identity and $\mathfrak{a}$ be a proper ideal of R. We introduce a notion of $\mathfrak{a}$-relative system of parameters and characterize them by using the notion of cohomological dimension. Also, we present a criterion of relative Cohen-Macaulay modules via relative system of parameters.

KEYWORDS AND PHRASES:

• Arithmetic rank
• cohomological dimension
• generalized fractions
• local cohomology
• relative Cohen-Macaulay module
• system of parameters

2010 Mathematics Subject Classification:

• 13C14
• 13C05
• 13D45

Acknowledgements

The authors thank Sara Saeedi Madani for introducing them to the references [2, 3] and [21].