Li, Tingyu; Zhang, Xia A further characterization of congruences on \(S\)-quantales. (Chinese. English summary) Zbl 1438.06050 J. South China Norm. Univ., Nat. Sci. Ed. 51, No. 1, 104-106 (2019). 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 Keywords:\(S\)-quantale; congruence; nucleus; quotient PDFBibTeX XMLCite \textit{T. Li} and \textit{X. Zhang}, J. South China Norm. Univ., Nat. Sci. Ed. 51, No. 1, 104--106 (2019; Zbl 1438.06050) Full Text: DOI