Geodesic
Flat modules and the behavior of a~standard basis relative to an extension of the ground ring
Fundamentalʹnaâ i prikladnaâ matematika, Tome 16 (2010) no. 8, pp. 69-72.

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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. 
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E. S. Golod. Flat modules and the behavior of a~standard basis relative to an extension of the ground ring. Fundamentalʹnaâ i prikladnaâ matematika, Tome 16 (2010) no. 8, pp. 69-72. http://geodesic.mathdoc.fr/item/FPM_2010_16_8_a5/

[1] Golod E. S., “Distributivnost, binarnye sootnosheniya i standartnye bazisy”, Fundament. i prikl. mat., 16:3 (2010), 127–134 | MR

[2] Golod E. S., “Standard bases and homology”, Algebra: Some Current Trends, Proc. of the 5th Nacional School in Algebra (Varna, Bulgaria, Sept. 24 – Oct. 4, 1986), Lect. Notes Math., 1352, eds. L. L. Avramov, K. B. Tchakerian, Springer, Berlin, 1988, 105–110 | MR