Geodesic
Semilocal semigroup rings
Glasgow mathematical journal, Tome 25 (1984) no. 1, pp. 37-44

Voir la notice de l'article provenant de la source Cambridge University Press

Semilocal and related classes of group rings have been investigated by many authors (cf. [10]). In particular, the following results have been obtained.Theorem A[4,10]. Let K be a field and G a group.(i) If ch K = 0, then K[G] is semilocal if and only if G is finite.(ii) If ch K = p>0 and G is locally finite, then K[G] is semilocal if and only if G contains a p-subgroup of finite index.In the case of semigroup rings some stronger conditions have been studied. Munn examined the semisimple artinian situation [6]. Zelmanov showed that if K[G]is artinian then G must be finite [11]. 
Okniński, Jan. Semilocal semigroup rings. Glasgow mathematical journal, Tome 25 (1984) no. 1, pp. 37-44. doi: 10.1017/S0017089500005401
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