Galois orders in skew monoid rings

We introduce a new class of noncommutative rings – Galois orders, realized as certain subrings of invariants in skew semigroup rings, and develop their structure theory. The class of Galois orders generalizes classical orders in noncommutative rings and contains many important examples, such as the Generalized Weyl algebras, the universal enveloping algebra of the general linear Lie algebra, associated Yangians and finite W-algebras.