Abstract
j ^)- Zimmermann-Huisgen [22, Corollary 2]showed that these are the left pure-semisimple rings defined below. And although leftpure-semisimple rings have many attractive features (see [15, p. 210]), it is not knownwhether they are all of finite representation type, that is, left artinian with only finitelymany indecomposable left modules.Auslander [1] showed that every left pure-semisimple artin algebra is of finiterepresentation type (an artin algebra is a ring which is finitely generated as a moduleover an artinian centre). If A is an artin algebra an
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