"Algebra structures on resolutions of rings defined by grade four almos" by Susan Palmer Slattery
 

Algebra structures on resolutions of rings defined by grade four almost complete intersections

Abstract

Let (R, m, k) be a local ring in which 2 is a unit and let J be an indeal in R. The minimal R-free resolution of R/J is called a DG-algebra if it has the structure of an associative, differential, graded commutative algebra over R. If J is a grade four almost complete intersection ideal in R, then J is necessarily linked to a grade four Gorenstein ideal I by a grade four complete intersection K. It is well known that the minimal R-free resolutions of R/I and R/K admit DG-algebra structures. In this paper, we show that if W denotes the image of the map TorR1(R/K, k) → TorR1(R/I, k) and W2 = 0 (for example, if K ⊆ mI), then the minimal R-free resolution of S = R/J has a DG-algebra structure. In the case where the ring R is regular local and K ⊆ mI we prove that the Poincaré series PNS(t) of every finitely generated S-module N is rational and the ring S satisfies the Eisenbud Conjecture.

Department(s)

Mathematics

Document Type

Article

DOI

https://doi.org/10.1006/jabr.1993.1144

Publication Date

8-1-1993

Journal Title

Journal of Algebra

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