Laurent Series Ring over Semiperfect Ring Can Not be Semiperfect

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Laurent Series Ring over Semiperfect Ring Can Not be Semiperfect

Ziembowski, Michał

Communications in algebra, 02/2014, Volume: 42, Issue: 2

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One of the main results of the article 2 says that, if a ring R is semiperfect and ϕ is an authomorphism of R, then the skew Laurent series ring R((x, ϕ)) 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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