A Complex of Modules and Its Applications to Local Cohomology and Extension Functors
DOI:
https://doi.org/10.7146/math.scand.a-22240Abstract
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,
- if projdimR(M)<∞, then injdimR(D(Hnm(M)))<∞, and
- if injdimR(M)<∞, then projdimR(D(Hnm(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, (k≥1), 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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