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University of Nebraska - Lincoln
Department of Mathematics: Dissertations, Theses, and Student Research
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Homological Characterizations Of Quasi-Complete Intersections, Jason M. Lutz
Homological Characterizations Of Quasi-Complete Intersections, Jason M. Lutz
Department of Mathematics: Dissertations, Theses, and Student Research
Let R be a commutative ring, (f) an ideal of R, and E = K(f; R) the Koszul complex. We investigate the structure of the Tate construction T associated with E. In particular, we study the relationship between the homology of T, the quasi-complete intersection property of ideals, and the complete intersection property of (local) rings.
Advisers: Luchezar L. Avramov and Srikanth B. Iyengar
Rigidity Of The Frobenius, Matlis Reflexivity, And Minimal Flat Resolutions, Douglas J. Dailey
Rigidity Of The Frobenius, Matlis Reflexivity, And Minimal Flat Resolutions, Douglas J. Dailey
Department of Mathematics: Dissertations, Theses, and Student Research
Let R be a commutative, Noetherian ring of characteristic p >0. Denote by f the Frobenius endomorphism, and let R^(e) denote the ring R viewed as an R-module via f^e. Following on classical results of Peskine, Szpiro, and Herzog, Marley and Webb use flat, cotorsion module theory to show that if R has finite Krull dimension, then an R-module M has finite flat dimension if and only if Tor_i^R(R^(e),M) = 0 for all i >0 and infinitely many e >0. Using methods involving the derived category, we show that one only needs vanishing for dim R +1 consecutive values of …