Ideals defining Gorenstein rings are (almost) never products
Craig Huneke
TL;DR
This paper proves that in unramified regular local rings, the quotient by the product of two proper ideals of height at least two is never Gorenstein, highlighting a structural limitation of such rings.
Contribution
It establishes a new non-existence result for Gorenstein quotients formed by products of ideals in unramified regular local rings.
Findings
S/IJ is not Gorenstein for proper ideals I, J of height ≥ 2 in unramified regular local rings.
Provides insight into the structure of Gorenstein rings and their ideals.
Highlights limitations on ideal products in certain regular local rings.
Abstract
This note proves that if S is an unramified regular local ring and I and J are proper ideals of height at least two, then S/IJ is never Gorenstein.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Algebraic structures and combinatorial models · Rings, Modules, and Algebras