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.
AMS Subject Classification
(1991): 13C10, 19A13, 14Q20, 03F65
Received February 18, 2013, and in revised form June 13, 2013. (Registered under 14/2013.)