Global dimension in serial rings (Q1061818)

Let R be an indecomposable basic serial Artin ring with n isomorphism classes of indecomposable projective modules. If the global dimension of R is finite then the author shows that the Loewy length of R is \(\leq 2n- 1\) and the global dimension of R is \(\leq 2n-2\). He also gives examples to show that these bounds are sharp.