On ideal and subalgebra coefficients in semigroup algebras |
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Authors: | Rainer Steinwandt |
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Affiliation: | 1. Institut für Algorithmen und Kognitive Systeme Prof. Dr. Th. Beth, Arbeitsgruppe Computeralgebra Fakult?t für Informatik, Universit?t Karlsruhe, Am Fasanengarten 5, 76128, Karlsruhe, Germany
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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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