GRÖBNER BASES FOR IDEALS IN UNIVARIATE POLYNOMIAL RINGS OVER VALUATION RINGS

Authors

  • M. Roslavcev University of Belgrade, Faculty of Mathematics, Studentski trg 16, Belgrade, Serbia Author

Keywords:

Valuation ring, zero-dimensional ring, Gröbner basis

Subjects:

13P10, 13F30

Abstract

Let V be a valuation ring such that dim(V)=0 and the annihilator of each element in V is finitely generated. In this paper it is proved that if I is a finitely generated ideal in the polynomial ring V[X], then there is a Gröbner basis for I. Also, an example of a zero-dimensional non-Noetherian valuation ring RM is presented, together with an example of finding a Gröbner basis for a certain ideal in a polynomial ring RM[X].

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Published

2021-07-15