FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1995, VOLUME 1, NUMBER 4, PAGES 1115-1118

Local semigroup rings

A.Ja.Ovsyannikov

The description of local semigroup algebras over a field of characteristic p (if p > 0, then semigroups are assumed to be locally finite) due to J. Okninsky (1984) is transferred to semigroup rings over non-radical rings. The following statement is proved. Let R be a ring, $R \ne J(R)$, $char R = 0$ ($char R = p > 1$), S be a semigroup (respectively, a locally finite semigroup). The semigroup ring R[S] is local [scalar local] if and only if R is such a ring and S is an ideal extension of a rectangular band (respectively of a completely simple semigroup over a p-group) by a locally nilpotent semigroup.

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