2012/01/15 by Fatemeh Mohammadi Aghjeh Mashhad, Mashhad, Fatemeh Mohammadi Aghjeh, Kamran Divaani-Aazar +1
Mathematics · #13D05 #13D25 #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #msc:13D05 #msc:13D25
paper · pdf · doi:10.48550/arxiv.1201.3067
It will be published in the journal of algebra and its applications
arxiv created 2012/01/15 · arxiv updated 2012/01/17
Let R be a commutative Noetherian ring, \fa an ideal of R and D(R) denote the derived category of R-modules. We investigate the theory of local homology in conjunction with Gorenstein flat modules. Let X be a homologically bounded to the right complex and Q a bounded to the right complex of Gorenstein flat R-modules such that Q and X are isomorphic in D(R). We establish a natural isomorphism \bf LΛ\fa(X)≃ Λ\fa(Q) in D(R) which immediately asserts that sup \bf LΛ\fa(X)≤ \GfdRX. This isomorphism yields several consequences. For instance, in the case R possesses a dualizing complex, we show that \GfdR \bf LΛ\fa(X)≤ \GfdRX. Also, we establish a criterion for regularity of Gorenstein local rings.