12 citations · 29 across the 3 of their papers we have counts for
6 papers · 1 filter
A central closure construction for certain extensions. Applications to Hopf algebra actions
Christian Lomp
Algebra extensions A < B where A is a left B-module such that the B-action extends the multiplication in A are ubiquitous. We encounter examples of such extensions in the study of…
Integrals in Hopf algebras over rings
Christian Lomp
Integrals in Hopf algebras are an essential tool in studying finite dimensional Hopf algebras and their action on algebras. Over fields it has been shown by Sweedler that the exist…
When is a smash product semiprime?
Christian Lomp
It is an open question whether the smash product of a semisimple Hopf algebra and a semiprime module algebra is semiprime. In this paper we show that the smash product of a commuta…
On the Splitting of the Dual Goldie Torsion Theory
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…
On Semilocal Modules and Rings
Christian Lomp
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 s…
Modules Whose Small Submodules Have Krull Dimension
Christian Lomp
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…