Is the lattice of torsion classes algebraic?
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- by Jorge Martinez PDF
- Proc. Amer. Math. Soc. 63 (1977), 9-14 Request permission
Abstract:
The answer is yes, if ... This note attempts to give amplification to the above statement, while at the same time arriving at a reasonable description of this lattice. The main theorem of the paper is no doubt the assertion that the lattice of torsion classes of lattice-ordered groups is completely distributive. The proof of this theorem depends on the notion of a value selector, and should not. As a consequence of this, one obtains a (local) decomposition theorem which is canonical (in every sense of the word) and always works.References
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P. Conrad, Lattice-ordered groups, Tulane Univ., 1970.
- Paul Conrad, Epi-archimedean groups, Czechoslovak Math. J. 24(99) (1974), 192–218. MR 347701
- Jorge Martinez, Unique factorization in partially ordered sets, Proc. Amer. Math. Soc. 33 (1972), 213–220. MR 292723, DOI 10.1090/S0002-9939-1972-0292723-5
- Jorge Martinez, Torsion theory for lattice-ordered groups, Czechoslovak Math. J. 25(100) (1975), 284–299. MR 389705
- Jorge Martinez, Torsion theory for lattice-ordered groups. II. Homogeneous $l$-groups, Czechoslovak Math. J. 26(101) (1976), no. 1, 93–100 (English, with Russian summary). MR 389706
Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 63 (1977), 9-14
- MSC: Primary 06A60
- DOI: https://doi.org/10.1090/S0002-9939-1977-0552652-0
- MathSciNet review: 0552652