zbMATH — the first resource for mathematics

Complete distributivity of lattice ordered groups and of vector lattices. (English) Zbl 0998.06013
Summary: In this paper we investigate the possibility of a regular embedding of a lattice-ordered group into a completely distributive vector lattice.

06F15 Ordered groups
06F20 Ordered abelian groups, Riesz groups, ordered linear spaces
Full Text: DOI EuDML
[1] S. J. Bernau: Unique representation of Archimedean lattice groups and normal Archimedean lattice rings. Proc. London Math. Soc. 15 (1965), 599-631. · Zbl 0134.10802
[2] G. Birkhoff: Lattice Theory. Revised Edition. American Mathematical Society, Providence, 1948.
[3] P. Conrad: Lattice Ordered Groups. Tulane University, 1970. · Zbl 0258.06011
[4] P. Conrad and D. McAlister: The completion of a lattice ordered group. J. Austral. Math. Soc. 9 (1969), 182-208. · Zbl 0172.31601
[5] J. Jakubík: Representation and extension of \(\ell \)-groups. Czechoslovak Math. J. 13 (1963), 267-283.
[6] J. Jakubík: Konvexe Ketten in \(\ell \)-Gruppen. Časopis pěst. matem. 84 (1959), 53-63. · Zbl 0083.01803
[7] J. Jakubík: Die Dedekindschen Schnitte im direkten Product von halbgeordneten Gruppen. Mat. fyz. časopis Slovenskej akad. vied 16 (1966), 329-336. · Zbl 0154.02602
[8] J. Jakubík: Distributivity in lattice ordered groups. Czechoslovak Math. J. 22 (1972), 108-125. · Zbl 0244.06014
[9] L. V. Kantorovich, B. Z. Vulikh and A. G. Pinsker: Functional Analysis in Semiordered Spaces. Moskva, 1950. · Zbl 0037.07201
[10] M. A. Lapellere and A. Valente: Embedding of Archimedean \(\ell \)-groups in Riesz spaces. Atti Sem. Mat. Fis. Univ. Modena 46 (1998), 249-254. · Zbl 0929.46009
[11] W. A. J. Luxemburg and A. C. Zaanen: Riesz Spaces, Vol. 1. North-Holland Publishing Company, Amsterdam, 1971. · Zbl 0231.46014
[12] F. Maeda and T. Ogasavara: Representation of vector lattices. J. Hiroshima Univ., Ser. A 12 (1942), 17-35.
[13] R. S. Pierce: Distributivity in Boolean algebras. Pacific. J. Math. 7 (1957), 983-992. · Zbl 0086.02803
[14] A. G. Pinsker: Extensions of semiordered groups and spaces. Uch. Zap. Leningrad. Gos. Ped. Inst. 86 (1949), 285-315.
[15] R. H. Redfield: Archimedean and basic elements in completely distributive lattice-ordered groups. Pacific. J. Math. 63 (1976), 247-253. · Zbl 0324.06007
[16] R. Sikorski: Boolean Algebras. Second Edition, Springer Verlag, Berlin, 1964. · Zbl 0123.01303
[17] E. C. Smith jr. and A. Tarski: Higher degrees of distributivity and completeness in Boolean algebras. Trans. Amer. Math. Soc. 84 (1957), 230-257. · Zbl 0092.03301
[18] B. Z. Vulikh: Introduction to the Theory of Semiordered Spaces. (In Russian; · Zbl 0101.08501
[19] K. Yosida: On the representation of the vector lattice. Proc. Acad. Tokyo 18 (1942), 339-342. · Zbl 0063.09070
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.