This article is cited in 5 papers

Primary orders with a finite numbers of indecomposable representations

Yu. A. Drozd, V. V. Kirichenko


Abstract: Let $\Lambda$ be a semisimple $Z$-ring and $C$ its center. Assume that for any prime ideal $\mathfrak p\subset C$ the ring $\Lambda_{\mathfrak p}$ is primary. Let $\overline\Lambda$ be the intersection of the maximal over-rings of $\Lambda$, $I=\overline\Lambda/\Lambda$ and $I'=\operatorname{rad}I$. We prove that $\Lambda$ has a finite number of indecomposable integral representations if and only if $\overline\Lambda$ is a hereditary ring, $I$ has two generators as a $\Lambda$-module, and $I'$ is cyclic.

UDC: 519.49

MSC: Primary 16A18, 16A64; Secondary 16A40

Received: 14.03.1972

 English version: Mathematics of the USSR-Izvestiya, 1973, 7:4, 711–732

Bibliographic databases:

• 
•