Journal of Mathematical Sciences

, Volume 185, Issue 2, pp 221–223 | Cite as

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

  • E. S. Golod


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.


Commutative Ring Broad Context Standard Basis Polynomial Ring Natural Image 
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  1. 1.
    E. S. Golod, “Standard bases and homology,” in: L. L. Avramov and K. B. Tchakerian, eds., Algebra: Some Current Trends. Proc. of the 5th National School in Algebra held in Varna, Bulgaria, Sept. 24 — Oct. 4, 1986, Lect. Notes Math., Vol. 1352, Springer, Berlin (1988), pp. 105–110.Google Scholar
  2. 2.
    E. S. Golod, “Distributivity, binary relations, and standard bases,” Fundam. Prikl. Mat., 16, No. 3, 127–134 (2010).MathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2012

Authors and Affiliations

  1. 1.Moscow State UniversityMoscowRussia

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