2014/04/15 by Cyrus Jalali, Jalali, Cyrus
Mathematics · #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1404.3982
openalex publication_date 2014/04/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let (R,\mathfrakm) be a commutative Noetherian local ring, \mathfraka be a proper ideal of R and M be an R-complex in D(R). We prove that if M\inDf_\sqsubset(R) (respectively, M\inDf_\sqsupset(R)), then idRRΓ_\mathfraka(M)=idR M (respectively, fdRRΓ_\mathfraka(M)=fdR M). Next, it is proved that the right derived section functor of a complex M\inD_\sqsubset(R) (R is not necessarily local) can be computed via a genuine left-bounded complex G≃ M of Gorenstein injective modules. We show that if R has a dualizing complex and M is an R-complex in Df_\square(R), then GfdRRΓ_\mathfraka(M)=GfdR M and GidRRΓ_\mathfraka(M)=GidR M. Also, we show that if M is a relative Cohen-Macaulay R-module with respect to \mathfraka (respectively, Cohen-Macaulay R-module of dimension n), then GfdRH^\mathrmhtM\mathfraka_\mathfraka(M)=GfdRM+n (respectively, GidRHn_\mathfrakm(M)=GidRM-n). The above results generalize some known results and provide characterizations of Gorenstein rings.