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

Author

Monceur, Samiha and Yengui, Ihsen

Subjects
*POLYNOMIALS, *VALUATION theory, *DIMENSIONAL analysis, *KRULL rings, *MATHEMATICAL analysis, QUESTIONS & answers
Abstract

Abstract: 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 ⩽1, 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-Gröbner and are studied in this paper. [Copyright &y& Elsevier]

Published
2012
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