Reducibility of parameter ideals in low powers of the maximal ideal

Document Type

Presentation Abstract

Presentation Date

4-5-2021

Abstract

It is well-known that a commutative, local, noetherian ring R is Gorenstein if and only if every parameter ideal of the ring is irreducible. A less well-known result due to Marley, Rogers, and Sakurai gives that there is an integer ℓ such that R is Gorenstein if and only if there exists an irreducible parameter ideal in the ℓ-th power of the maximal ideal. The proof of this result gives that ℓ is the smallest integer such that a certain map of Ext modules is surjective after taking socles. Our work investigates upper bounds on this integer ℓ. In this talk, we'll focus on historical context and examples where the ring R is a quotient of a power series ring.

Additional Details

April 5, 2021 at 3:00 p.m. via Zoom

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