Characterisations of Generalised Uniserial Algebras. III

Abstract

Let A be a finite dimensional algebra with identity element over a field. A is generalised uniserial if every primitive left ideal and every primitive right ideal of A has only one compositions series. In the previous papers in this series (6, 7) generalised uniserial algebras have been characterised as algebras all of whose residue class algebras are of certain types. The purpose of this paper is to extend the earlier results by showing that in order that A be generalised uniserial it is sufficient to require weaker conditions on merely a finite sequence of residue class algebras of A.