@article {
author = {Hager, Anthony W. and McGovern, Warren Wm.},
title = {The projectable hull of an archimedean $\ell$-group with weak unit},
journal = {Categories and General Algebraic Structures with Applications},
volume = {7},
number = {Special Issue on the Occasion of Banaschewski's 90th Birthday (II)},
pages = {165-179},
year = {2017},
publisher = {Shahid Beheshti University},
issn = {2345-5853},
eissn = {2345-5861},
doi = {},
abstract = {The much-studied projectable hull of an $\ell$-group $G\leq pG$ is an essential extension, so that, in the case that $G$ isĀ archimedean with weak unit, ``$G\in {\bf W}$", we have for the Yosida representation spaces a ``covering map" $YG \leftarrow YpG$. We have earlier \cite{hkm2} shown that (1) this cover has a characteristic minimality property, and that (2) knowing $YpG$, one can write down $pG$. We now show directly that for $\mathscr{A}$, the boolean algebra in the power set of the minimal prime spectrum $Min(G)$, generated by the sets $U(g)=\{P\in Min(G):g\notin P\}$ ($g\in G$), the Stone space $\mathcal{A}\mathscr{A}$ is a cover of $YG$ with the minimal property of (1); this extends the result from \cite{bmmp} for the strong unit case. Then, applying (2) gives the pre-existing description of $pG$, which includes the strong unit description of \cite{bmmp}. The present methods are largely topological, involving details of covering maps and Stone duality.},
keywords = {Archimedean $l$-group,vector lattice,Yosida representation,minimal prime spectrum,principal polar,projectable,principal projection property},
url = {http://cgasa.sbu.ac.ir/article_46629.html},
eprint = {http://cgasa.sbu.ac.ir/article_46629_aaedb6eda82247753a33798657cb5075.pdf}
}