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We compute the monoid V (LK(E)) of isomorphism classes of finitely generated projective modules over certain graph algebras LK(E), and we show that this monoid satisfies the refinement property and separative cancellation. We also show that there is a natural isomorphism between the lattice of graded ideals of LK(E) and the lattice of order-ideals of V(More)
Let E be a row-finite quiver and let E0 be the set of vertices of E; consider the adjacency matrix N ′ E = (nij) ∈ Z(E0×E0), nij = #{ arrows from i to j}. Write N E and 1 for the matrices ∈ Z (E0×E0\Sink(E)) which result from N ′t E and from the identity matrix after removing the columns corresponding to sinks. We consider the K-theory of the Leavitt(More)
We prove a cancellation theorem for simple refinement monoids satisfying the weak comparability condition, first introduced by K.C. O’Meara in the context of von Neumann regular rings. This result is then applied to von Neumann regular rings and C∗-algebras of real rank zero via the monoid of isomorphism classes of finitely generated projective modules.(More)
Replacing invertibility with quasi-invertibility in Bass’ first stable range condition we discover a new class of rings, the QB−rings. These constitute a considerable enlargement of the class of rings with stable rank one (B−rings), and include examples like EndF(V ), the ring of endomorphisms of a vector space V over some field F, and B(F), the ring of all(More)
A longstanding open problem in the theory of von Neumann regular rings is the question of whether every directly finite simple regular ring must be unit-regular. Recent work on this problem has been done by P. Menal, K.C . O'Meara, and the authors. To clarify some aspects of these new developments, we introduce and study the notion of almost isomorphism(More)
We compute the Hochschild homology of Leavitt path algebras over a field k. As an application, we show that L2 and L2 ⊗ L2 have different Hochschild homologies, and so they are not Morita equivalent; in particular they are not isomorphic. Similarly, L∞ and L∞ ⊗ L∞ are distinguished by their Hochschild homologies and so they are not Morita equivalent either.(More)