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The rank condition and strong rank conditions for Ore extensions
Karl Lorensen, Johan Öinert
Let be a ring, a ring endomorphism, and a -derivation. We establish that the Ore extension satisfies the rank condition if and only if d…
Rank conditions and amenability for rings associated to graphs
Karl Lorensen, Johan Öinert
We study path rings, Cohn path rings, and Leavitt path rings associated to directed graphs, with coefficients in an arbitrary ring . For each of these types of rings, we stipula…
Generating numbers of rings graded by amenable and supramenable groups
Karl Lorensen, Johan Öinert
A ring has {\it unbounded generating number} (UGN) if, for every positive integer , there is no -module epimorphism . For a ring $R=\bigoplus_{g\in G} R_g…
Group-graded rings satisfying the strong rank condition
Peter Kropholler, Karl Lorensen
A ring satisfies the {\it strong rank condition} (SRC) if, for every natural number , the free -submodules of all have rank . Let be a group and a r…