We develop the theory of “branch algebras”, which are infinitedimensional associative algebras that are isomorphic, up to taking subrings of finite codimension, to a matrix ring over themselves. The main examples come from groups acting on trees. In particular, for every field k we construct a k-algebra K which • is finitely generated and infinite-dimensional, but has only finite-dimensional qu...

In this paper we introduce the Pivoting M-tree (PM-tree), a metric access method combining M-tree with the pivot-based approach. While in M-tree a metric region is represented by a hyper-sphere, in PM-tree the shape of a metric region is determined by intersection of the hyper-sphere and a set of hyper-rings. The set of hyper-rings for each metric region is related to a fixed set of pivot objec...

We develop the theory of “branch algebras”, which are infinitedimensional associative algebras that are isomorphic, up to taking subrings of finite codimension, to a matrix ring over themselves. The main examples come from groups acting on trees. In particular, we construct an algebra over the field of two elements, that is finitely generated, prime, infinite-dimensional but with all proper quo...