Automorphism-invariant modules Page 30 Contemporary Mathematics Volume 634 , 2015
http://dx. doi. org/10.1090/conm/634/12688 Automorphism-Invariant Modules Pedro A. Guil …

In this paper we develop a general theory of modules which are invariant under
automorphisms of their covers and envelopes. When applied to specific cases like injective …

The unit graph of a ring R, denoted G (R), is the simple graph defined on the elements of R
with an edge between vertices x and y iff x+ y is a unit of R. In this paper, we prove that the …

We use the type theory for rings of operators due to Kaplansky to describe the structure of
modules that are invariant under automorphisms of their injective envelopes. Also, we …

Let $ R $ be a ring. The unit graph of $ R $, denoted by $ G (R) $, is the simple graph
defined on all elements of $ R $, and where two distinct vertices $ x $ and $ y $ are linked by …

Cet article est un bref survey de l'étude des anneaux engendrés par leurs unités. The study
of rings generated additively by their units started in 1953-1954 when KG Wolfson [24] and …

" The study of modules which are invariant under the action of certain subsets of the
endomorphism ring of their injective envelope can be drawn back to the pioneering work of …

We establish commutativity theorems for certain classes of rings in which every invertible
element is central, or, more generally, in which all invertible elements commute with one …

In this paper, we study rings that are additively generated by units. We prove that if the
identity in a ring with stable range one is a sum of two units, then every (von Neumann) …

We give an overview on recent results concerning additive unit representations. Furthermore
the solutions of some open questions are included. The central problem is whether and how …