New characterizations of Artinian modules and hereditary rings. (Neue Charakterisierungen von Artinschen Moduln und hereditären Ringen.) (German) Zbl 0744.16012
Let \(R\) be an associative ring with 1. The author proves that a left \(R\)- module \(M\) is Artinian iff every non-empty set of finitely cogenerated factor modules of \(M\) has a maximal element, and that \(R\) is left hereditary iff in every projective left \(R\)-module \(M\) the intersection \(U\cap V\) of two direct summands \(U\) and \(V\) of \(M\) is also a direct summand of \(M\).
Reviewer: W.Müller (Bayreuth)
MSC:
16P20 | Artinian rings and modules (associative rings and algebras) |
16D40 | Free, projective, and flat modules and ideals in associative algebras |