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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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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