On the leading terms ideals of polynomial ideals over a valuation ring

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• 作者：Samiha Monceur ; Ihsen Yengui ; ^{ihsen.yengui@fss.rnu.tn}
• 关键词：13C10 ; 19A13 ; 14Q20 ; 03F65
• 刊名：Journal of Algebra
• 出版年：2012
• 出版时间：1 February 2012
• 年：2012
• 卷：351
• 期：1
• 页码：382-389
• 全文大小：143 K

文摘

We construct an example of a finitely generated ideal I of , where V is a one-dimensional valuation ring, whose leading terms ideal is not finitely generated. This gives a negative answer to the open question of whether if V is a valuation ring with Krull dimension ?, then for any finitely generated ideal I of , the leading terms ideal of I is also finitely generated. The valuation rings satisfying this latter property will be called 1-Gr?bner and are studied in this paper.