Maximal ordered groupoids and a Galois correspondence for inverse semigroup orthogonal actions (Q6050138)

The authors introduce maximal ordered groupoids and construct equivalent conditions for being maximal and then produce other results that incorporate maximality in different settings. A number of correspondence theorems are demonstrated that relate different sets of wide and maximal, ordered subgroupoids. Using the Ehresmann-Schein-Nambooripad theorem, which establishes a one-to-one correspondence between inverse semigroups and a class of ordered groupoids, the authors prove a Galois correspondence for the case of inverse semigroups acting orthogonally on commutative rings.