[go: up one dir, main page]

 

  Previous |  Up |  Next

Article

Keywords:
lattice ordered group; $\ell $-ideal; congruence lattice; disjoint subset
Summary:
In the present note we characterize finite lattices which are isomorphic to the congruence lattice of an abelian lattice ordered group.
References:
[1] G. Birkhoff: Lattice Theory. Revised Edition, Providence, 1948. MR 0029876 | Zbl 0033.10103
[2] P. Conrad: The structure of a lattice ordered group with a finite number of disjoint elements. Michigan Math. J. 7 (1960), 171–182. DOI 10.1307/mmj/1028998387 | MR 0116059 | Zbl 0103.01501
[3] P. Conrad: Lattice Ordered Groups. Tulane University, 1970. Zbl 0258.06011
[4] G. Grätzer: On the congruence lattice of a lattice. In: The Dilworth Theorems. Selected Papers of Robert P. Dilworth, K. Bogart, R. Freese, J. Kung (eds.), Birkhäuser Verlag, Basel, 1990, pp. 460–464. MR 1111511
[5] G. Grätzer, E. T. Schmidt: On congruence lattices of lattices. Acta Math. Acad. Sci. Hungar. 13 (1962), 179–185. DOI 10.1007/BF02033636 | MR 0139551
[6] K. Iwasawa: On linearly ordered groups. J. Math. Soc. Japan 1 (1948), 1–9. DOI 10.2969/jmsj/00110001 | MR 0028313 | Zbl 0038.01301
[7] J. Jakubík: On lexico extensions of lattice ordered groups. Math. Slovaca 33 (1983), 81–84. MR 0689282
[8] M. Ploščica, J. Tůma, F. Wehrung: Congruence lattices of free lattices in non-distributive varieties. Colloq. Math. 76 (1998), 269–278. DOI 10.4064/cm-76-2-269-278 | MR 1618712
Partner of
EuDML logo