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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.)
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