Isometries of multilattice groups. (English) Zbl 0538.06018

The authors show that the results on the relation between isometries and direct decompositions of lattice ordered groups can be extended to hold for abelian distributive multilattice groups. They note that the question of whether the assumption of distributivity or commutativity can be dropped remains open.
Reviewer: G.P.Barker


06F20 Ordered abelian groups, Riesz groups, ordered linear spaces
06D05 Structure and representation theory of distributive lattices
20F60 Ordered groups (group-theoretic aspects)
Full Text: EuDML


[1] M. Benado: Sur la théorie de la divisibilité. Acad. R. P. Romine, Bui. Sti. Sect. Mat. Fiz. 6, (1954), 263-270. · Zbl 0057.25301
[2] P. Conrad: Lattice ordered groups. Tulane University 1970. · Zbl 0258.06011
[3] Л. Фукс: Частично упорядоченные алгебраические системы. Москва 1965. · Zbl 1099.01519
[4] J. Jakubík: Isometries of lattice ordered groups. Czech. Math. J. 30 (105) (1980), 142- 152. · Zbl 0436.06013
[5] J. Jakubík: On isometries of non-abelian lattice ordered groups. Math. Slovaca 31, (1981), 171-175.
[6] Я. Якубик: Прямые разложения частично упорядоченных групп. II Czech. Math. J. 11 (86), (1961), 490-513. · Zbl 1160.68305
[7] D. B. McAlister: On multilattice groups. Proc. Cambridge Philos. Soc. 61 (1965), 621-638. · Zbl 0135.06203
[8] D. B. McAlister: On multilattice groups II. Proc. Cambridge Philos. Soc. 62 (1966), 149- 164. · Zbl 0138.02702
[9] W. B. Powell: On isometries in abelian lattice ordered groups. Preprint, Oklahoma State University. · Zbl 0614.06012
[10] K. L. Swamy: Isometries in autometrized lattice ordered groups. Algebra Univ. 8 (1977), 58-64. · Zbl 0457.06015
[11] K. L. Swamy: Isometries in autometrized lattice ordered groups, II. Math. Seminar Notes Kobe Univ. 5 (1977), 211-214. · Zbl 0457.06015
[12] J. Trias: Lattice isometries in Riesz spaces. Preprint, Univ. Politecnica Barcelona, 1981. · Zbl 0515.06014
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