Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Quantifier elimination for algebraic $D$-groups
HTML articles powered by AMS MathViewer

by Piotr Kowalski and Anand Pillay PDF
Trans. Amer. Math. Soc. 358 (2006), 167-181 Request permission


We prove that if $G$ is an algebraic $D$-group (in the sense of Buium over a differentially closed field $(K,\partial )$ of characteristic $0$, then the first order structure consisting of $G$ together with the algebraic $D$-subvarieties of $G, G\times G,\dots$, has quantifier-elimination. In other words, the projection on $G^{n}$ of a $D$-constructible subset of $G^{n+1}$ is $D$-constructible. Among the consequences is that any finite-dimensional differential algebraic group is interpretable in an algebraically closed field.
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 32C38, 03C60
  • Retrieve articles in all journals with MSC (2000): 32C38, 03C60
Additional Information
  • Piotr Kowalski
  • Affiliation: Department of Mathematics, Wrocław University, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
  • MR Author ID: 658570
  • Anand Pillay
  • Affiliation: Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801
  • MR Author ID: 139610
  • Received by editor(s): January 5, 2004
  • Published electronically: January 21, 2005
  • Additional Notes: The first author was supported by a postdoc under NSF Focused Research Grant DMS 01-00979 and the Polish KBN grant 2 P03A 018 24
    The second author was partially supported by NSF grants DMS 00-70179 and DMS 01-00979
  • © Copyright 2005 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 358 (2006), 167-181
  • MSC (2000): Primary 32C38, 03C60
  • DOI:
  • MathSciNet review: 2171228