Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Is the lattice of torsion classes algebraic?


Author: Jorge Martinez
Journal: Proc. Amer. Math. Soc. 63 (1977), 9-14
MSC: Primary 06A60
MathSciNet review: 0552652
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 06A60

Retrieve articles in all journals with MSC: 06A60


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0552652-0
PII: S 0002-9939(1977)0552652-0
Keywords: Torsion class, torsion radical, value selector, algebraic lattice, compact element
Article copyright: © Copyright 1977 American Mathematical Society