Note on regular and coregular sequences

Document Type : Research Paper

Author

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

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.

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References

[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.
Algebraic Structures and Their Applications
Volume 4, Issue 2
November 2017
Pages 39-43

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