It is proved that if (S,?) is a proper *-semigroup and if D is 0-characteristic integral domain then (D[S],?) is nil-semisimple provided that S is finite or i ∈ D.Let (S,?) be a finite proper *-semigroup and F be a finite field of characteristic p such that (F[S],?) is a proper *-ring. Then F[S] is a direct product of fields and 2×2 matrix rings over fields. Furthermore, p≠2,p≠1 mod 4.
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机译：证明了如果（S ,?）是一个适当的*-半群，并且如果D是0特征积分域，那么只要S是有限的或i∈D，（D [S] ,?）是nil-半简单。 S ，?）是有限的适当的*-半群，F是特征p的有限域，使得（F [S] ,?）是适当的*-环。那么F [S]是场和场上2×2矩阵环的直接积。此外，p≠2，p≠1 mod 4。
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