arXiv subjects
Publications and source records attributed to Christian Lomp.
The splitting of the Goldie (or singular) torsion theory has been extensively studied. Here we determine an appropriate dual Goldie torsion theory, discuss its splitting and answer in the negative a question proposed by Ozcan and Harmanci as to whether the splitting of the dual Goldie torsion theory implies the ring to be quasi-Frobenius.
The main aim of this paper is to show that an AB5*-module whose small submodules have Krull dimension has a radical having Krull dimension. The proof uses the notion of dual Goldie dimension.
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).