論Gorenstein理想

Abstract

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。

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.