Branch rings, thinned rings, tree enveloping rings

. R A ] 8 O ct 2 00 4 BRANCH RINGS , THINNED RINGS , TREE ENVELOPING RINGS

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...

. R A ] 2 2 N ov 2 00 4 BRANCH RINGS , THINNED RINGS , TREE ENVELOPING RINGS

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...

ar X iv : m at h / 04 10 22 6 v 3 [ m at h . R A ] 1 7 A ug 2 00 5 BRANCH RINGS , THINNED RINGS , TREE ENVELOPING RINGS

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...

Evidence from Tree rings

Introduction Conclusions References

Differential Polynomial Rings of Triangular Matrix Rings