Previous |  Up |  Next

Article

Keywords:
lattice ordered group; wreath product; affine completeness
Summary:
Let $\Delta $ and $H$ be a nonzero abelian linearly ordered group or a nonzero abelian lattice ordered group, respectively. In this paper we prove that the wreath product of $\Delta $ and $H$ fails to be affine complete.
References:
[1] Conrad, P.: Lattice Ordered Groups. Tulane University New Orleans (1970). Zbl 0258.06011
[2] Jakubík, J.: Affine completeness of complete lattice ordered groups. Czechoslovak Math. J. 45 (1995), 571-576. MR 1344522
[3] Jakubík, J.: On the affine completeness of lattice ordered groups. Czechoslovak Math. J. 54 (2004), 423-429. DOI 10.1023/B:CMAJ.0000042381.83544.a7 | MR 2059263
[4] Jakubík, J.: Affine completeness and lexicographic product decompositions of abelian lattice ordered groups. Czechoslovak Math. J. 55 (2005), 917-922. DOI 10.1007/s10587-005-0075-0 | MR 2184372
[5] Jakubík, J., Csontóová, M.: Affine completeness of projectable lattice ordered groups. Czechoslovak Math. J. 48 (1998), 359-363. DOI 10.1023/A:1022849823068 | MR 1624264
[5] Kaarli, K., Pixley, A. F.: Polynomial Completeness in Algebraic Systems. Chapman-Hall London-New York-Washington (2000). MR 1888967
Partner of
EuDML logo