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Winter 2020 Resolutions of length four which are differential graded algebras
Andrew R. Kustin
J. Commut. Algebra 12(4): 509-538 (Winter 2020). DOI: 10.1216/jca.2020.12.509

Abstract

Let P be a commutative Noetherian ring and F be a self-dual acyclic complex of finitely generated free P-modules. Assume that F has length four and F0 has rank one. We prove that F can be given the structure of a differential graded algebra with divided powers; furthermore, the multiplication on F exhibits Poincaré duality. This result is already known if P is a local Gorenstein ring and F is a minimal resolution. The purpose of the present paper is to remove the unnecessary hypotheses that P is local, P is Gorenstein, and F is minimal.

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Andrew R. Kustin. "Resolutions of length four which are differential graded algebras." J. Commut. Algebra 12 (4) 509 - 538, Winter 2020. https://doi.org/10.1216/jca.2020.12.509

Information

Received: 21 June 2019; Revised: 26 August 2019; Accepted: 28 August 2019; Published: Winter 2020
First available in Project Euclid: 5 January 2021

MathSciNet: MR4194939
Digital Object Identifier: 10.1216/jca.2020.12.509

Subjects:
Primary: 13D02, 16E45

Rights: Copyright © 2020 Rocky Mountain Mathematics Consortium

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Vol.12 • No. 4 • Winter 2020
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