A negative answer to a question about leading terms ideals of polynomial ideals

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• 作者：Emmanuel Pola^a ; ^b ; ^{pdemma@yahoo.fr} ; Ihsen Yengui^b ; ^{ihsen.yengui@fss.rnu.tn}
• 关键词：13C10 ; 19A13 ; 14Q20 ; 03F65
• 刊名：Journal of Pure and Applied Algebra
• 出版年：2012
• 出版时间：November, 2012
• 年：2012
• 卷：216
• 期：11
• 页码：2432-2435
• 全文大小：195 K

文摘

We construct an example of a finitely generated ideal of , where is a one-dimensional domain, whose leading terms ideal is not finitely generated. This gives a negative answer to the open question of whether if is a domain with Krull dimension ?, then for any finitely generated ideal of , the leading terms ideal of is also finitely generated. Moreover, as a positive part of our answer, we prove that for any one-dimensional domain and any , the ideal of generated by the leading terms of is finitely generated.