The Globalization problem for inner automorphisms and Skolem-Noether theorems
Abstract
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 a ring with local units. We
show that every inner automorphism is locally inner but the converse is false, even if
the automorphism is “piecewise” inner. On the other hand, we construct a large class
of rings for which every locally inner automorphism is actually inner. Finally we obtain
some Skolem-Noether type Theorems for infinite matrix and triangular matrix rings.
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