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

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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]**G. Birkhoff,*Lattice theory*, Amer. Math. Soc. Colloq. Publ., vol. 25, Amer. Math. Soc., Providence, R. I., 1967. MR**0227053 (37:2638)****[2]**P. Conrad,*Lattice-ordered groups*, Tulane University Lecture Notes, 1970.**[3]**W. C. Holland,*Varieties of l-groups are torsion classes*, Czechoslovak Math. J. (to appear). MR**518135 (80b:06017)****[4]**O. Kenny, Dissertation, University of Kansas, 1975.**[5]**J. Martinez,*Archimedean-like classes of lattice-ordered groups*, Trans. Amer. Math. Soc.**186**(1973), 33-49. MR**0332614 (48:10940)****[6]**-,*Torsion theory for lattice-ordered groups*, Czechoslovak Math. J.**25**(**100**) (1975), 284-299. MR**0389705 (52:10536)****[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.

Retrieve articles in *Transactions of the American Mathematical Society*
with MSC:
06F15

Retrieve articles in all journals with MSC: 06F15

Additional Information

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

Article copyright:
© Copyright 1980
American Mathematical Society