FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2010, VOLUME 16, NUMBER 8, PAGES 69-72

**Flat modules and the behavior of a standard basis relative to an
extension of the ground ring**

E. S. Golod

Abstract

View as HTML
View as gif image

The property of a generating set of a polynomial ideal or
of an ideal of a free associative algebra over a commutative
ring to be its Gröbner basis is kept by a flat (but not any)
extension of the ground ring.
The converse is proved in the broader context of standard bases for
filtered modules.

Location: http://mech.math.msu.su/~fpm/eng/k10/k108/k10806h.htm

Last modified: December 5, 2011