A Complex of Modules and Its Applications to Local Cohomology and Extension Functors

Authors

  • Kamal Bahmanpour

DOI:

https://doi.org/10.7146/math.scand.a-22240

Abstract

Let (R,m) be a commutative Noetherian complete local ring and let M be a non-zero Cohen-Macaulay R-module of dimension n. It is shown that,

  1. if projdimR(M)<, then injdimR(D(Hnm(M)))<, and
  2. if injdimR(M)<, then projdimR(D(Hnm(M)))<,
where D():=HomR(,E) denotes the Matlis dual functor and E:=ER(R/m) is the injective hull of the residue field R/m.

Also, it is shown that if (R,m) is a Noetherian complete local ring, M is a non-zero finitely generated R-module and x1,,xk, (k1), is an M-regular sequence, then D(Hk(x1,,xk)(D(Hk(x1,,xk)(M))))M. In particular, AnnHk(x1,,xk)(M)=AnnM. Moreover, it is shown that if R is a Noetherian ring, M is a finitely generated R-module and x1,,xk is an M-regular sequence, then Extk+1R(R/(x1,,xk),M)=0.

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Published

2015-09-28

How to Cite

Bahmanpour, K. (2015). A Complex of Modules and Its Applications to Local Cohomology and Extension Functors. MATHEMATICA SCANDINAVICA, 117(1), 150–160. https://doi.org/10.7146/math.scand.a-22240

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Articles