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be a decomposition of A into direct sum of indecomposable left ideals; the elemeats eKΛ (l<^/c^k, l^i<^f(κ)) are mutually orthogonal primitive idempotents of A such that AeK)%=AeλiJ if and only if tc = λ. We put eκ>1 = eκ, *Σ]ιeK)l=Eκ; E = *ΣiKEκ is the unit element of A. Further, let eKttf Sκ, etc. have the same meaning to A as eκ>ι, Eκ, etc. to A. For a subset S of A we denote the left [right] annihilators of S by lΛ(S) lrA(S)2; the notations £?(*), IN(*) etc. may be defined similarly. Remembering theorem 1 of [2], we shall assume in this note that both A and A are bound rings and that M=lN(N) = rN(N) is contained in N . Then by theorem 2 of [2] A—A/N is isomorphic to A=A/N; moreover, there is a (unique) 1-1 correspondence between the simple constituents of A and those of A. So that wemay assume, after a suitable reordering, that AK—AEK corresponds to AK—AEK in this correspondence (l^κ^k).

Remarks concerning two quasi-Frobenius rings with isomorphic radicals