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 Mat. Zametki, 2003, Volume 74, Issue 4, Pages 529–537 (Mi mz287)

Radical Semigroup Rings and the Thue–Morse Semigroup

I. B. Kozhukhov

Moscow State Institute of Electronic Technology (Technical University)

Abstract: Let $R$ be an associative ring with unit, let $S$ be a semigroup with zero, and let $RS$ be a contracted semigroup ring. It is proved that if $RS$ is radical in the sense of Jacobson and if the element 1 has infinite additive order, then $S$ is a locally finite nilsemigroup. Further, for any semigroup $S$, there is a semigroup $T\supset S$ such that the ring $RT$ is radical in the Brown–McCoy sense. Let $S$ be the semigroup of subwords of the sequence $abbabaabbaababbab...$, and let $F$ be the two-element field. Then the ring $FS$ is radical in the Brown–McCoy sense and semisimple in the Jacobson sense.

DOI: https://doi.org/10.4213/mzm287

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English version:
Mathematical Notes, 2003, 74:4, 502–509

Bibliographic databases:

UDC: 512.552.7
Revised: 04.11.2002

Citation: I. B. Kozhukhov, “Radical Semigroup Rings and the Thue–Morse Semigroup”, Mat. Zametki, 74:4 (2003), 529–537; Math. Notes, 74:4 (2003), 502–509

Citation in format AMSBIB
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