Maximal Ordered Groupoids and a Galois Correspondence for Inverse Semigroup Orthogonal Actions

Maximal Ordered Groupoids and a Galois Correspondence for Inverse Semigroup Orthogonal Actions

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 semigr...

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Veröffentlicht in:Applied categorical structures 2023-10, Vol.31 (5), Article 31
Hauptverfasser: Lautenschlaeger, Wesley G., Tamusiunas, Thaísa
Format: Artikel
Sprache:eng
Schlagworte:
Convex and Discrete Geometry
Geometry
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Rings (mathematics)
Semigroups
Theory of Computation
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Zusammenfassung: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.
ISSN:0927-2852
1572-9095
DOI:10.1007/s10485-023-09742-z