This paper investigates the ring-theoretic similarities and the cate- gorical dissimilarities between the ring RFM(R) of row finite matrices and the ring RCFM(R) of row and column finite matrices. For example, we prove ...

We investigate the circumstances under which an inner automorphism of a ring with local units can be built from “local” information. Specifically, we consider three natural “inner” type properties for an automorphism of ...

Let Λ be a tiled R-order. We give a description of AutR(Λ) as the semidirect product of Inn(Λ) and a certain subgroup of Aut(Q(Λ)), where Q(Λ) is the link graph of Λ. Additionally, we give criteria for determining when ...

We characterize when a crossed product order over a maximal order in a central simple algebra by a finite group is hereditary. We need only concentrate on the cases when the group acts as inner automorphisms and when ...

Let P and P’ be finite preordered sets, and let R be a ring for which the number of nonzero summands in a direct decomposition of the regular module RR is bounded. We show that if the incidence rings I(P;R) and I(P’;R) ...

For a ring A with local units we investigate unital overrings T of A, and compare the automorphism groups Aut(A) and Aut(T ).

Let R be a complete local Dedekind domain with quotient field K and let A be a local R-order in a separable K-algebra. This paper classifies those orders A such that every indecomposable R-torsionfree A-module is isomorphic ...

We develop the foundations for graded equivalence theory and apply them to investigate properties such as primeness, finite representation type, and vertex theory of graded rings. The key fact that we prove is that, for ...