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Let R be a semiprime algebra over a field F, and let I be either an ideal of R or a right ideal with zero left annihilator in R. Let and
, where a
i
, b
i
∈ R. Suppose that dim
F
B
1 < ∞ (|B
1| < ∞). Then dim
F
B
2 < ∞ and dim
F
B
1 = dim
F
B
2 (resp. |B
2| < ∞ and |B
1| = |B
2|).
#Communicated by E. Puczylowski.
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