Abstract
For a finite dimensional algebra A, with 0<ϕdim(A)=m<∞, we show that there always exist modules M and N, such that ϕ(M)=1, and ϕ(N)=m−1. On the other hand, we give an example of an algebra such that not every value between 1 and its ϕ-dimension is reached by the ϕ function. We call such values gaps, and show that the algebras with gaps verifies the finitistic dimension conjecture.
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