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

E. S. Golod

M. V. Lomonosov Moscow State University

Abstract: 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.

UDC: 512.552

 English version: Journal of Mathematical Sciences (New York), 2012, 185:2, 221–223

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