Results in Mathematics

, Volume 39, Issue 1–2, pp 183–187 | Cite as

On ideal and subalgebra coefficients in semigroup algebras

  • Rainer Steinwandt


Let k[S] be a semigroup algebra with coefficients in a commutative field k, and let U be a one-sided ideal in k[S] or a k-subalgebra of k[S], It is proven that there exists a smallest subfield k′ ≤ k such that U as a one-sided ideal resp. as a k-algebra can be generated by elements in k′[S]. By means of an example it is shown that the straightforward extension of this result to finitely generated commutative k-algebras is not valid.


Field of definition semigroup algebra one-sided ideal k-subalgebra 

AMS Subject Classification

16S36 20M25 


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  1. [1]
    André Weil. Foundations of Algebraic Geometry, volume 29 of Colloquium publications. American Mathematical Society, Providence, Rhode Island, 1946.Google Scholar
  2. [2]
    Serge Lang. Introduction to Algebraic Geometry. Number 5 in Interscience Tracts in Pure and Applied Mathematics. Interscience Publishers, New York, London, 1958.zbMATHGoogle Scholar
  3. [3]
    Lorenzo Robbiano and Moss Sweedler. Ideal and Subalgebra Coefficients. Proc. Am. Math. Soc., 126(8):2213–2219, 1998.zbMATHCrossRefGoogle Scholar
  4. [4]
    Jörn Müller-Quade and Martin Rötteler. Deciding Linear Disjointness of Finitely Generated Fields. In Oliver Gloor, editor, Proceedings of the 1998 International Symposium on Symbolic and Algebraic Computation, pages 153-160. The Association for Computing Machinery, Inc. (ACM), August 1998.Google Scholar
  5. [5]
    Rainer Steinwandt. Decomposing systems of polynomial equations. In Victor G. Ganzha, Ernst W. Mayr, and Evgenii V. Vorozhtsov, editors, Computer Algebra in Scientific Computing CASC ’99. Proceedings of the Second Workshop on Computer Algebra in Scientific Computing, Munich, May 31–June 4, 1999, pages 387-407, Berlin; Heidelberg, 1999. Springer.Google Scholar
  6. [6]
    A. H. Clifford and G. B. Preston. The Algebraic Theory of Semigroups, volume I, no. 7 of Mathematical Surveys. American Mathematical Society, Providence, Rhode Island, second edition, 1964.Google Scholar

Copyright information

© Birkhäuser Verlag, Basel 2001

Authors and Affiliations

  • Rainer Steinwandt
    • 1
  1. 1.Institut für Algorithmen und Kognitive Systeme Prof. Dr. Th. Beth, Arbeitsgruppe Computeralgebra Fakultät für InformatikUniversität KarlsruheKarlsruheGermany

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