| Summary: | 碩士 === 國立臺灣大學 === 數學研究所 === 99 === 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.
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