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Fundamentalnaya i Prikladnaya Matematika, 2010, Volume 16, Issue 8, Pages 69–72 (Mi fpm1378)  
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
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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.
English version:
Journal of Mathematical Sciences (New York), 2012, Volume 185, Issue 2, Pages 221–223
DOI: https://doi.org/10.1007/s10958-012-0911-3
Bibliographic databases:
Document Type: Article
UDC: 512.552
Language: Russian
Citation: E. S. Golod, “Flat modules and the behavior of a standard basis relative to an extension of the ground ring”, Fundam. Prikl. Mat., 16:8 (2010), 69–72; J. Math. Sci., 185:2 (2012), 221–223
Citation in format AMSBIB
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\by E.~S.~Golod
\paper Flat modules and the behavior of a~standard basis relative to an extension of the ground ring
\jour Fundam. Prikl. Mat.
\yr 2010
\vol 16
\issue 8
\pages 69--72
\mathnet{http://mi.mathnet.ru/fpm1378}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2869834}
\transl
\jour J. Math. Sci.
\yr 2012
\vol 185
\issue 2
\pages 221--223
\crossref{https://doi.org/10.1007/s10958-012-0911-3}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84866320892}
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    		Фундаментальная и прикладная математика
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