Geodesic
Radical Semigroup Rings and the Thue--Morse Semigroup
Matematičeskie zametki, Tome 74 (2003) no. 4, pp. 529-537.

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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. 
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     title = {Radical {Semigroup} {Rings} and the {Thue--Morse} {Semigroup}},
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I. B. Kozhukhov. Radical Semigroup Rings and the Thue--Morse Semigroup. Matematičeskie zametki, Tome 74 (2003) no. 4, pp. 529-537. http://geodesic.mathdoc.fr/item/MZM_2003_74_4_a5/

[1] Kozhukhov I. B., “Technique of semigroup ring theory: Artinian, perfect and semiprimary semigroup rings”, J. Math. Sci., 97:6 (1999), 4527–4537 | DOI | MR | Zbl

[2] Zhuchin A. V., “O polulokalnykh polugruppovykh koltsakh”, Fundamentalnaya i prikladnaya matem., 5:1 (1999), 139–147 | MR | Zbl

[3] Okninski J., “On regular semigroup rings”, Proc. Roy. Soc. Edinburgh, 99A (1984), 145–151 | MR

[4] de Luca A., Varicchio S., “Some combinatorial properties of the Thue–Morse sequence and a problem in semigroups”, Theor. Comput. Sci., 63:3 (1989), 333–348 | DOI | MR | Zbl