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On ideal and subalgebra coefficients in semigroup algebras

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Abstract

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.

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  1. Institut für Algorithmen und Kognitive Systeme Prof. Dr. Th. Beth, Arbeitsgruppe Computeralgebra Fakultät für Informatik, Universität Karlsruhe, Am Fasanengarten 5, 76128, Karlsruhe, Germany

    Rainer Steinwandt

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  1. Rainer Steinwandt
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Steinwandt, R. On ideal and subalgebra coefficients in semigroup algebras. Results. Math. 39, 183–187 (2001). https://doi.org/10.1007/BF03322683

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  • DOI: https://doi.org/10.1007/BF03322683

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