Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9497189 | Journal of Pure and Applied Algebra | 2005 | 29 Pages |
Abstract
A ãâ¨,0ã-semilattice is ultraboolean, if it is a directed union of finite Boolean ãâ¨,0ã-semilattices. We prove that every distributive ãâ¨,0ã-semilattice is a retract of some ultraboolean ãâ¨,0ã-semilattice. This is established by proving that every finite distributive ãâ¨,0ã-semilattice is a retract of some finite Boolean ãâ¨,0ã-semilattice, and this in a functorial way. This result is, in turn, obtained as a particular case of a category-theoretical result that gives sufficient conditions, for a functor Î , to admit a right inverse. The particular functor Î used for the abovementioned result about ultraboolean semilattices has neither a right nor a left adjoint.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Friedrich Wehrung,