Date of Award

1-1-2017

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

College/School/Department

Department of Mathematics and Statistics

Content Description

1 online resource (ii, 25 pages)

Dissertation/Thesis Chair

Alexandre B Tchernev

Committee Members

Antun Milas, Marco Varisco, Anupam Srivastav

Keywords

Schur functions, Noetherian rings, Torsion free Abelian groups

Subject Categories

Mathematics | Physical Sciences and Mathematics

Abstract

Let $R$ be a local Noetherian commutative ring and $I$ an ideal with projective dimension less than or equal to 1. Necessary and sufficient conditions were provided in \cite{T2007} for a symmetric power $S_kI$ of an ideal of projective dimension 1 to be torsion free, where $k \geq 2$. We extend this result to symmetric powers and a broad class of Schur functors of finitely generated $R$-modules with projective dimension 1. While doing so, we also study the structure of Schur complexes from \cite{ABW1982}, and provide necessary and sufficient conditions for the acyclicity of the Schur complex by computing the ideals of maximal minors of the differentials from the Schur complex.

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