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A further characterization of congruences on \(S\)-quantales. (Chinese. English summary) Zbl 1438.06050

Summary: Let \(S\) be a posemigroup. Motivated by the algebraic method of quantale theory, congruences on an \(S\)-quantale are studied. The minimum congruence generated by an arbitrary binary relation in a given \(S\)-quantale \({Q_S}\) is characterized, the 1-1 correspondence between nuclei and congruences on \({Q_S}\) is obtained, and the relationship between congruences on \({Q_S}\) and relative quotients derived from nuclei is studied.

MSC:

06F07 Quantales
06B10 Lattice ideals, congruence relations
06F05 Ordered semigroups and monoids
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