Archimedean vector lattices generated by two elements
Roger D. Bleier
Proc. Amer. Math. Soc. 39 (1973), 1-9
Full-text PDF Free Access
Similar Articles |
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.
A. Baker, Free vector lattices, Canad. J. Math.
20 (1968), 58–66. MR 0224524
Birkhoff, Lattice theory, Third edition. American Mathematical
Society Colloquium Publications, Vol. XXV, American Mathematical Society,
Providence, R.I., 1967. MR 0227053
D. Bleier, Free vector lattices, Trans. Amer. Math. Soc. 176 (1973), 73–87. MR 0311541
(47 #103), http://dx.doi.org/10.1090/S0002-9947-1973-0311541-8
P. Conrad, Lattice ordered groups, Tulane University, New Orleans, La., 1970.
Yosida, On vector lattice with a unit, Proc. Imp. Acad. Tokyo
17 (1941), 121–124. MR 0005795
- K. Baker, Free vector lattices, Canad. J. Math. 20 (1968), 58-66. MR 37 #123. MR 0224524 (37:123)
- G. Birkhoff, Lattice theory, Amer. Math. Soc. Colloq. Publ., vol. 25, Amer. Math. Soc., Providence, R.I., 1967. MR 37 #2638. MR 0227053 (37:2638)
- R. Bleier, Free vector lattices, Trans. Amer. Math. Soc. 176 (1973), 73-87. MR 0311541 (47:103)
- P. Conrad, Lattice ordered groups, Tulane University, New Orleans, La., 1970.
- K. Yosida, On a vector lattice with unit, Proc. Japan Acad. 17 (1941), 121-124. MR 3, 210. MR 0005795 (3:210a)
Retrieve articles in Proceedings of the American Mathematical Society
Retrieve articles in all journals
© Copyright 1973 American Mathematical Society