The $HSP$-Classes of Archimedean $l$-groups with Weak Unit

Banaschewski, Bernhard, and Hager, Anthony. "The $HSP$-Classes of Archimedean $l$-groups with Weak Unit." Annales de la faculté des sciences de Toulouse Mathématiques 19.S1 (2010): 13-24. <http://eudml.org/doc/115862>.

@article{Banaschewski2010,
abstract = {$W$ denotes the class of abstract algebras of the title (with homomorphisms preserving unit). The familiar $H, S,$ and $P$ from universal algebra are here meant in $W$. $\mathbb\{Z\}$ and $\mathbb\{R\}$ denote the integers and the reals, with unit 1, qua$W$-objects. $V$ denotes a non-void finite set of positive integers. Let $\mathcal\{G\}\subseteq W$ be non-void and not $\lbrace \lbrace 0\rbrace \rbrace $. We show(1), and(2) if and only if Our proofs are, for the most part, simple calculations. There is no real use of methods of universal algebra (e.g., free objects), and only one restricted use of representation theory (Yosida). Note that (1) implies the basic fact that $HSP\mathbb\{R\}= W$ (which can be proved in several ways). Note that (2) contrasts $W$ with $\mathcal\{C\} = $ archimedean $l$-groups, and $\mathcal\{C\} =$ abelian $l$-groups, where $HSP\mathbb\{Z\}= \mathcal\{C\}$ in each case.},
affiliation = {Department of Mathematics, McMaster University, Hamilton, Ontario 68S4K1 Canada; Department of Mathematics and Computer Science Wesleyan University, Middletown, CT 06459 USA},
author = {Banaschewski, Bernhard, Hager, Anthony},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
language = {eng},
month = {4},
number = {S1},
pages = {13-24},
publisher = {Université Paul Sabatier, Toulouse},
title = {The $HSP$-Classes of Archimedean $l$-groups with Weak Unit},
url = {http://eudml.org/doc/115862},
volume = {19},
year = {2010},
}

TY - JOUR
AU - Banaschewski, Bernhard
AU - Hager, Anthony
TI - The $HSP$-Classes of Archimedean $l$-groups with Weak Unit
JO - Annales de la faculté des sciences de Toulouse Mathématiques
DA - 2010/4//
PB - Université Paul Sabatier, Toulouse
VL - 19
IS - S1
SP - 13
EP - 24
AB - $W$ denotes the class of abstract algebras of the title (with homomorphisms preserving unit). The familiar $H, S,$ and $P$ from universal algebra are here meant in $W$. $\mathbb{Z}$ and $\mathbb{R}$ denote the integers and the reals, with unit 1, qua$W$-objects. $V$ denotes a non-void finite set of positive integers. Let $\mathcal{G}\subseteq W$ be non-void and not $\lbrace \lbrace 0\rbrace \rbrace $. We show(1), and(2) if and only if Our proofs are, for the most part, simple calculations. There is no real use of methods of universal algebra (e.g., free objects), and only one restricted use of representation theory (Yosida). Note that (1) implies the basic fact that $HSP\mathbb{R}= W$ (which can be proved in several ways). Note that (2) contrasts $W$ with $\mathcal{C} = $ archimedean $l$-groups, and $\mathcal{C} =$ abelian $l$-groups, where $HSP\mathbb{Z}= \mathcal{C}$ in each case.
LA - eng
UR - http://eudml.org/doc/115862
ER -