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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     author = {E. S. Golod},
     title = {Flat modules and the behavior of a~standard basis relative to an extension of the ground ring},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {69--72},
     publisher = {mathdoc},
     volume = {16},
     number = {8},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2010_16_8_a5/}
}
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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/