Abstract
We introduce maximal ordered groupoids and study some of their properties. Also, we use the Ehresmann–Schein–Nambooripad Theorem, which establishes a one-to-one correspondence between inverse semigroups and a class of ordered groupoids, to prove a Galois correspondence for the case of inverse semigroups acting orthogonally on commutative rings.
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Lautenschlaeger, W.G., Tamusiunas, T. Maximal Ordered Groupoids and a Galois Correspondence for Inverse Semigroup Orthogonal Actions. Appl Categor Struct 31, 31 (2023). https://doi.org/10.1007/s10485-023-09742-z
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DOI: https://doi.org/10.1007/s10485-023-09742-z