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A Galois correspondence theorem is proved for the case of inverse semigroupsacting orthogonally on commutative rings as a consequence of the Galoiscorrespondence theorem for groupoid actions. To this end, we use a classicresult of inverse semigroup theory that establishes a one-to-one correspondencebetween inverse semigroups and inductive groupoids.

Galois Theory for Inverse Semigroup Orthogonal Actions