TY - JOUR
ID - 46629
TI - The projectable hull of an archimedean $ell$-group with weak unit
JO - Categories and General Algebraic Structures with Applications
JA - CGASA
LA - en
SN - 2345-5853
AU - Hager, Anthony W.
AU - McGovern, Warren Wm.
AD - Department of Mathematics and CS, Wesleyan University, Middletown, CT 06459.
AD - H. L. Wilkes Honors College, Florida Atlantic University, Jupiter, FL 33458.
Y1 - 2017
PY - 2017
VL - 7
IS - Special Issue on the Occasion of Banaschewski's 90th Birthday (II)
SP - 165
EP - 179
KW - Archimedean $l$-group
KW - vector lattice
KW - Yosida representation
KW - minimal prime spectrum
KW - principal polar
KW - projectable
KW - principal projection property
DO -
N2 - The much-studied projectable hull of an $ell$-group $Gleq pG$ is an essential extension, so that, in the case that $G$ isĀ archimedean with weak unit, ``$Gin {bf W}$", 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 $U(g)={Pin Min(G):gnotin P}$ ($gin G$), 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.
UR - http://cgasa.sbu.ac.ir/article_46629.html
L1 - http://cgasa.sbu.ac.ir/article_46629_aaedb6eda82247753a33798657cb5075.pdf
ER -