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
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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.

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Keywords: Torsion class, torsion radical, value selector, algebraic lattice, compact element
Article copyright: © Copyright 1977 American Mathematical Society