Note on regular and coregular sequences

Document Type : Research Paper

Author

Department of Mathematics, Sanandaj Branch, Islamic Azad University, Sanandaj, Iran

10.29252/asta.4.2.39

Abstract

Let $R$ be a commutative Noetherian ring and let $M$ be a finitely generated $R$-module. If $I$ is an ideal of $R$ generated by $M$-regular sequence, then we study the vanishing of the first $\Tor$ functors. Moreover, for Artinian modules and coregular sequences we examine the vanishing of the first $\Ext$ functors.

Keywords


[1] W. Bruns and J. Herzog, Cohen-Macaulay rings, Cambridge University Press, Cambridge, UK, (1998).
[2] H. Matsumura, Commutative ring theory, Cambridge University Press, Cambridge, UK, (1986).
[3] A. Ooishi, Matlis duality and width of a module, Hiroshima Math. J., 6 (1976), 573-587.