Geodesic
On semilocal semigroup rings
Fundamentalʹnaâ i prikladnaâ matematika, Tome 5 (1999) no. 1, pp. 139-147.

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The approach for study semilocal semigroup rings over non-radical rings based on description the structure of semigroup on the whole is suggested. The following main statement is proved. Let $R$ be a ring, $\overline R=R/J(R)\ne 0$, $S$ be a semigroup with zero $z$. The semigroup ring $RS$ is semilocal if and only if: $(i)$ $R$ is semilocal; $(ii)$ there exists a chain of ideals $\{z\}=S_0\subset S_1\subset\ldots\subset S_n=S$ such that $S_i/S_{i-1}$, $1\le i\le n$, are nil or completely $0$-simple; $(iii)$ the contracted semigroup rings $R_0(S_i/S_{i-1})$, are semilocal. 
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     author = {A. V. Zhuchin},
     title = {On semilocal semigroup rings},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {139--147},
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     volume = {5},
     number = {1},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_1999_5_1_a9/}
}
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A. V. Zhuchin. On semilocal semigroup rings. Fundamentalʹnaâ i prikladnaâ matematika, Tome 5 (1999) no. 1, pp. 139-147. http://geodesic.mathdoc.fr/item/FPM_1999_5_1_a9/