The fundamental theorem on torsion classes of lattice-ordered groups
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- by Jorge Martinez PDF
- Trans. Amer. Math. Soc. 259 (1980), 311-317 Request permission
Abstract:
This paper generalizes the earlier notion of a torsion class to a setting where its significance can be fully realized. The dual notion of a torsion-free class is herein defined and the fundamental Connection Theorem is proved. In addition, a few restrictions are considered, in particular, how to view the application of the main theorem to the hereditary classes.References
- Garrett Birkhoff, Lattice theory, 3rd ed., American Mathematical Society Colloquium Publications, Vol. XXV, American Mathematical Society, Providence, R.I., 1967. MR 0227053 P. Conrad, Lattice-ordered groups, Tulane University Lecture Notes, 1970.
- W. Charles Holland, Varieties of $l$-groups are torsion classes, Czechoslovak Math. J. 29(104) (1979), no. 1, 11–12. MR 518135 O. Kenny, Dissertation, University of Kansas, 1975.
- Jorge Martinez, Archimedean-like classes of lattice-ordered groups, Trans. Amer. Math. Soc. 186 (1973), 33–49. MR 332614, DOI 10.1090/S0002-9947-1973-0332614-X
- Jorge Martinez, Torsion theory for lattice-ordered groups, Czechoslovak Math. J. 25(100) (1975), 284–299. MR 389705 —, A general theory of torsion classes for lattice-ordered groups, University of Florida notes. H. Neumann, Varieties of groups, Ergebnisse der Math, und ihrer Grenzgebiete, Band 37, Springer-Verlag, Berlin and New York, 1967.
Additional Information
- © Copyright 1980 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 259 (1980), 311-317
- MSC: Primary 06F15
- DOI: https://doi.org/10.1090/S0002-9947-1980-0561839-7
- MathSciNet review: 561839