Approximating rings with local units via automorphisms
Let \(A\) be a ring with local units. An approximation of \(A\) is an overring \(T\) containing \(A\) such that \(A=ATA\) and for each \(0\neq t\in T\) there exist \(a\), \(b\) with \(atb\neq 0\). There are three classical unital approximations of \(A\), namely, the Dorroh extension \(C(A)\), the endomorphism ring \(E(A)=\text{End}(_AA)\), and the translation hull \(Q(A)\). If \(T\) is a unital approximation of \(A\), then the restriction induces a homomorphism between the automorphism groups \(\Aut(T)\) and \(\Aut(A)\). The aim of the paper is a comparison of these automorphism groups by using the canonical restriction homomorphism.
scientific article; zbMATH DE number 1355012