The Gorenstein Property of Semigroup Rings
Date Issued
2011
Date
2011
Author(s)
Chang, Chih-Wei
Abstract
This thesis is divided into two parts. In the first part, we present necessary preliminaries and prove the main result of Stanley [10] : for a semigroup Γ ⊂ Zn≥0, the semigroup ring k[Γ] is Gorenstein if and only if the Poincare series F(k[Γ],λ) is symmetric.
In the second part, we discuss the symmetricity of a semigroup Γ ⊂ Zn ≥0 such that k[Γ] is integral closed. In the case n = 2, we will characterize symmetricity in several aspects. In the case n = 3, with some additional restrictions, we still have a similar result.
Subjects
semigroup
semigroup ring
poincare series
Gorenstein ring
Frobenius problem
Type
thesis
File(s)![Thumbnail Image]()
Loading...
Name
ntu-100-R96221026-1.pdf
Size
23.54 KB
Format
Adobe PDF
Checksum
(MD5):9dcf915839cc9edd5abbf1b6917be058