Comments on monoreflections in unital archimedean lattice-ordered groups and rings

Document Type

Article

Publication Date

12-15-2016

Abstract

In quite general concrete categories, the monoreflections which are H-closed (closed under homomorphic image) are the “naturally occuring” ones, since each is comprised of objects closed under some family of functorial implicit operations. In the specific categories under consideration here, we have earlier shown the class of H-closed monoreflections to be a set, indeed, relatively small. In spite, or because of that very few non-H-closed monoreflections have been exhibited, in fact, none in the categories considered here. We shall exhibit many and assuming no measurable cardinal, a proper class.

Publication Source (Journal or Book title)

Quaestiones Mathematicae

First Page

1093

Last Page

1099

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