Semilattice congruences viewed from quasi-orders
HTML articles powered by AMS MathViewer
- by Takayuki Tamura PDF
- Proc. Amer. Math. Soc. 41 (1973), 75-79 Request permission
Abstract:
Let $S$ be a semigroup. This paper proves that the smallest semilattice congruence ${\rho _0}$ containing a compatible binary relation $\xi$ on $S$ equals the natural equivalence of the smallest lower-potent positive quasi-order ${\sigma _0}$ containing $\xi$.References
- Mohan S. Putcha, Minimal sequences in semigroups, Trans. Amer. Math. Soc. 189 (1974), 93–106. MR 338233, DOI 10.1090/S0002-9947-1974-0338233-4
- Takayuki Tamura, The theory of construction of finite semigroups. I, Osaka Math. J. 8 (1956), 243–261. MR 83497
- Takayuki Tamura, Another proof of a theorem concerning the greatest semilattice-decomposition of a semigroup, Proc. Japan Acad. 40 (1964), 777–780. MR 179282
- T. Tamura, The theory of operations on binary relations, Trans. Amer. Math. Soc. 120 (1965), 343-358; errata, ibid. 123 (1965), 273. MR 0209375, DOI 10.1090/S0002-9947-1965-0209375-3
- Takayuki Tamura, Note on the greatest semilattice decomposition of semigroups, Semigroup Forum 4 (1972), 255–261. MR 307990, DOI 10.1007/BF02570795 —, Quasi-orders, generalized archimedeaness and semilattice decomposition (to appear).
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 41 (1973), 75-79
- MSC: Primary 20M10
- DOI: https://doi.org/10.1090/S0002-9939-1973-0333048-X
- MathSciNet review: 0333048