STABILITY AND BUCHBERGER CRITERION FOR STANDARD BASES IN POWER-SERIES RINGS

We prove that the property of a finite set of formal power series to be a standard basis of the ideal it generates is locally stable in the space of admissible term orders. Consequently, universal standard bases exist. We give a criterion for an ideal basis to be a standard basis which is an analogue to Buchberger's 'critical pair criterion' for Groebner bases. © 1990.