ACTA issues

Gröbner rings

Emmanuel Pola, Ihsen Yengui

Acta Sci. Math. (Szeged) 80:3-4(2014), 363-372

Abstract. In this paper, Gröbner rings are studied. In particular, we prove constructively that Gröbner rings are stably coherent. Moreover, we prove that a valuation ring is Gröbner if and only if it is both coherent and archimedean, answering (in the multivariate case) an open question.

DOI: 10.14232/actasm-013-514-3

AMS Subject Classification (1991): 13C10, 19A13, 14Q20, 03F65

Keyword(s): Gröbner bases, coherent rings, monomial orders, Syzygy modules

Received February 18, 2013, and in revised form June 13, 2013. (Registered under 14/2013.)