On Semilocal Modules and Rings
| dc.creator | Lomp, Christian | |
| dc.date | 1998-07-21 | |
| dc.date.accessioned | 2026-07-07T05:25:27Z | |
| dc.date.available | 2026-07-07T05:25:27Z | |
| dc.description | It is well-known that a ring R is semiperfect if and only if R as a left (or as a right) R-module is a supplemented module. Considering weak supplements instead of supplements we show that weakly supplemented modules M are semilocal (i.e., M/Rad(M) is semisimple) and that R is a semilocal ring if and only if R as a left (or as a right) R-module is weakly supplemented. In this context the notion of finite hollow dimension (or finite dual Goldie dimension) of modules is of interest and yields a natural interpretation of the Camps-Dicks characterization of semilocal rings. Finitely generated modules are weakly supplemented if and only if they have finite hollow dimension (or are semilocal). | |
| dc.description | to appear in Communications in Algebra | |
| dc.identifier | https://arxiv.org/abs/math/9807113 | |
| dc.identifier | http://arxiv.org/abs/math/9807113 | |
| dc.identifier | Communications in Algebra, 27(4), 1921-1935 (1999) | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/77186 | |
| dc.subject | Rings and Algebras | |
| dc.subject | 16L30 (primary) ; 16P20 ; 16D90 (secondary) | |
| dc.title | On Semilocal Modules and Rings | |
| dc.type | text |