Archimedean vector lattices generated by two elements
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- by Roger D. Bleier PDF
- Proc. Amer. Math. Soc. 39 (1973), 1-9 Request permission
Abstract:
The class of vector lattices referred to in the title is investigated from the point of view of the free vector lattice on two elements. It is shown that only three of these vector lattices are indecomposable. They are then described. A complete structure theorem for projective vector lattices generated by two elements is proved. The arguments depend throughout on the precise description of the free vector lattice which is established in the first section.References
- Kirby A. Baker, Free vector lattices, Canadian J. Math. 20 (1968), 58–66. MR 224524, DOI 10.4153/CJM-1968-008-x
- Garrett Birkhoff, Lattice theory, 3rd ed., American Mathematical Society Colloquium Publications, Vol. XXV, American Mathematical Society, Providence, R.I., 1967. MR 0227053
- Roger D. Bleier, Free vector lattices, Trans. Amer. Math. Soc. 176 (1973), 73–87. MR 311541, DOI 10.1090/S0002-9947-1973-0311541-8 P. Conrad, Lattice ordered groups, Tulane University, New Orleans, La., 1970.
- Kôsaku Yosida, On vector lattice with a unit, Proc. Imp. Acad. Tokyo 17 (1941), 121–124. MR 5795
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 39 (1973), 1-9
- MSC: Primary 06A65
- DOI: https://doi.org/10.1090/S0002-9939-1973-0329997-9
- MathSciNet review: 0329997