Laurent Series Ring over Semiperfect Ring Can Not be Semiperfect |
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Authors: | Michał Ziembowski |
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Affiliation: | 1. Faculty of Mathematics and Information Science , Warsaw University of Technology , Warsaw , Poland m.ziembowski@mini.pw.edu.pl |
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Abstract: | One of the main results of the article [2 Sonin , K. I. ( 1996 ). Semiprime and semiperfect rings of Laurent series . Mathematical Notes 60 : 222 – 226 .[Crossref], [Web of Science ®] , [Google Scholar]] says that, if a ring R is semiperfect and ? is an authomorphism of R, then the skew Laurent series ring R((x, ?)) is semiperfect. We will show that the above statement is not true. More precisely, we will show that, if the Laurent series ring R((x)) is semilocal, then R is semiperfect with nil Jacobson radical. |
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Keywords: | Nil Jacobson radical Semilocal ring Skew Laurent series ring Semiperfect ring |
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