A representation theorem for semilattices
HTML articles powered by AMS MathViewer
- by D. A. Bredikhin PDF
- Proc. Amer. Math. Soc. 90 (1984), 219-220 Request permission
Abstract:
We prove that every semilattice $(L, \wedge )$ admits an embedding $Q$ into the set $R(X)$ of all partial orders on some set $X$ such that for all $a$, $b \in L$, $Q(a \wedge b) = Q(a) \cap Q(b)$ and if $a \vee b$ exists then also $Q(a \vee b) = Q(b) \circ Q(a)$.References
- D. A. Bredihin and B. M. Schein, Representations of ordered semigroups and lattices by binary relations, Colloq. Math. 39 (1978), no. 1, 1–12. MR 507256, DOI 10.4064/cm-39-1-1-12
- Bjarni Jónsson, On the representation of lattices, Math. Scand. 1 (1953), 193–206. MR 58567, DOI 10.7146/math.scand.a-10377
- B. M. Schein, A representation theorem for lattices, Algebra Universalis 2 (1972), 177–178. MR 306065, DOI 10.1007/BF02945026
Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 90 (1984), 219-220
- MSC: Primary 06A12; Secondary 06B15
- DOI: https://doi.org/10.1090/S0002-9939-1984-0727237-7
- MathSciNet review: 727237