論Gorenstein理想

On Gorenstein Ideals

林泰均(Tai-Jiun Lin)

指導教授 ： 朱樺

國立臺灣大學/理學院/數學研究所/碩士(2007年)

https://doi.org/10.6342/NTU.2007.00779

摘要

本論文中，我們算出某些情況下Gorenstein理想的生成元。我們對二項式的情況重給簡潔的証明並討論三項式的某一類情況:
x^{ rho}y_{1}^{sigma_{1}}cdots y_{s}^{sigma_{s}}
z_{1}^{ tau_{1}}cdots z_{t}^{ tau_{t}}(x^{w}-y_{1}^{u_{1}} cdots y_{s}^{u_{s}}-z_{1}^{v_{1}}cdots z_{t}^{v_{t}}) 。我們只給出生成元的領導項，而整個生成元可以由證明的過程寫出。

關鍵字

Gorenstein

並列摘要

In this paper, we compute generators of Gorenstein ideals in some special case. We give another proof of the binomial case and discuss a trinomial of the form
x^{ rho}y_{1}^{sigma_{1}}cdots y_{s}^{sigma_{s}}
z_{1}^{ tau_{1}}cdots z_{t}^{ tau_{t}}(x^{w}-y_{1}^{u_{1}} cdots y_{s}^{u_{s}}-z_{1}^{v_{1}}cdots z_{t}^{v_{t}}) . We just give the leading terms of the generators. And the entire generators can be written out in the process of the proofs.

並列關鍵字

Gorenstein

參考文獻

Department of Mathematics, National Taiwan University.

Bass, H. (1962), “Injective dimension in Noetherian rings”, Trans. Amer. Math.

(1963), “On the ubiquity of gorenstein rings”, Math. Zeitschrift, 82, 8–28.

Eisenbud, D. (1996), Commutative Algebra with a View Toward Algebraic Geometry, New York: Springer Verlag.

Gorenstein, D. (1952), “An arithmetic theory of adjoint plane curves”, Trans. Amer. Math. Soc., 72, 414–436.