Abstract
Following Eisenbud and Griffith [3,4], we say that a ring R is serial if both RR and RR are direct sums of uniserial modules of finite length. Serial rings were introduced by Nakayama[14], who established the well-known theorem that each module such a ring is a direct sum of factor module of indecomposable projective modules and conversely. With each indecomposable serial ring R, Kupisch [10] associated a series P1,…,Pn of left indecomposable projective modules, which is called a left Kupisch series for R. Let c(i) be the composition length of Pi. Then the series (c(l),…,c(n)) is called the left admissible sequence corresponding to a left Kupisch series P1,…,Pn.
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