Geodesic
Local contracted semigroup rings
Fundamentalʹnaâ i prikladnaâ matematika, Tome 7 (2001) no. 3, pp. 939-944 
A. V. Zhuchin. Local contracted semigroup rings. Fundamentalʹnaâ i prikladnaâ matematika, Tome 7 (2001) no. 3, pp. 939-944. http://geodesic.mathdoc.fr/item/FPM_2001_7_3_a23/
@article{FPM_2001_7_3_a23,
     author = {A. V. Zhuchin},
     title = {Local contracted semigroup rings},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {939--944},
     year = {2001},
     volume = {7},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2001_7_3_a23/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The local contracted semigroup rings $R_0S$ over non-radical rings $R$ ($\overline R=R/J(R)\ne\{0\}$) are under consideration. The following main statement is proved. Let $R$ be a ring, $\overline R\ne\{0\}$, $S$ be a semigroup with zero. The ring $R_0S$ is local if and only if: (i) there exists a nil ideal $N\subseteq S$ such that $S/N\cong T^0$ is a semigroup $T$ (without zero) with adjoint zero; (ii) $RT$ is local, $R_0N$ is radical.