On ideal and subalgebra coefficients in semigroup algebras
- 25 Downloads
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.
KeywordsField of definition semigroup algebra one-sided ideal k-subalgebra
AMS Subject Classification16S36 20M25
Unable to display preview. Download preview PDF.
- André Weil. Foundations of Algebraic Geometry, volume 29 of Colloquium publications. American Mathematical Society, Providence, Rhode Island, 1946.Google Scholar
- 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
- 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
- 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