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
Bass, H. (1962), “Injective dimension in Noetherian rings”, Trans. Amer. Math.
(1963), “On the ubiquity of gorenstein rings”, Math. Zeitschrift, 82, 8–28.
Department of Mathematics, National Taiwan University.
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.
延伸閱讀
- Chen, C. A. (2005). 零維 Gorenstein 理想 [master's thesis, National Taiwan University]. Airiti Library. https://doi.org/10.6342/NTU.2005.00710
- 黃韻慈、王鴻祥、洪唯軒、孫芃（2015）。踏上大師之路－以生態系統架構設計師生涯歷程資料庫。載於中華民國設計學會（主編），中華民國設計學會研究論文（頁315-320）。中華民國設計學會。https://doi.org/10.6668/CID-IDSFC.201505.0047
- 李益美（2023）。心靈饗宴／為理想而堅定前行。臺灣現代詩，(74)，98-99。https://www.airitilibrary.com/Article/Detail?DocID=18164617-N202306140004-00071
- 葉慈（2016）。「理想」的團契。新使者，(152)，72-73。https://www.airitilibrary.com/Article/Detail?DocID=a0000496-201502-201603020032-201603020032-72-73
- Sheets, R. W. (1981). PARTIAL HENSELIZATIONS. International Journal of Mathematics and Mathematical Sciences, 1981(), 691-701. https://doi.org/10.1155/S0161171281000525