The fundamental theorem on torsion classes of lattice-ordered groups

Author:
Jorge Martinez

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

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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.

**[1]**Garrett Birkhoff,*Lattice theory*, Third edition. American Mathematical Society Colloquium Publications, Vol. XXV, American Mathematical Society, Providence, R.I., 1967. MR**0227053****[2]**P. Conrad,*Lattice-ordered groups*, Tulane University Lecture Notes, 1970.**[3]**W. Charles Holland,*Varieties of 𝑙-groups are torsion classes*, Czechoslovak Math. J.**29(104)**(1979), no. 1, 11–12. MR**518135****[4]**O. Kenny, Dissertation, University of Kansas, 1975.**[5]**Jorge Martinez,*Archimedean-like classes of lattice-ordered groups*, Trans. Amer. Math. Soc.**186**(1973), 33–49. MR**0332614**, https://doi.org/10.1090/S0002-9947-1973-0332614-X**[6]**Jorge Martinez,*Torsion theory for lattice-ordered groups*, Czechoslovak Math. J.**25(100)**(1975), 284–299. MR**0389705****[7]**-,*A general theory of torsion classes for lattice-ordered groups*, University of Florida notes.**[8]**H. Neumann,*Varieties of groups*, Ergebnisse der Math, und ihrer Grenzgebiete, Band 37, Springer-Verlag, Berlin and New York, 1967.

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DOI:
https://doi.org/10.1090/S0002-9947-1980-0561839-7

Article copyright:
© Copyright 1980
American Mathematical Society