Mathematical Structures: History of Abelian ordered groups

# History of Abelian ordered groups

 Revision 2 . . July 25, 2004 3:12 pm by Jipsen Revision 1 . . July 25, 2004 12:09 pm by Jipsen

Difference (from prior major revision) (no other diffs)

Changed: 28,29c28,29

Changed: 31c31
 \abbreviation{Abbr}
 \abbreviation{AoGrp}

Changed: 34,39c34
 A ... is a structure $\mathbf{A}=\langle A,...\rangle$ of type $\langle ...\rangle$ such that $\langle A,...\rangle$ is a \href{Name_of_class.pdf}{name of class} $op_1$ is (name of property): $axiom_1$
 An abelian ordered group is an \href{Ordered_groups.pdf}{ordered group} $\mathbf{A}=\langle A,+,-,0,\le\rangle$ such that

Changed: 41c36
 $op_2$ is ...: $...$
 $+$ is commutative: $x+y=y+x$

Changed: 50,51c45,46
 Let $\mathbf{A}$ and $\mathbf{B}$ be ... . A morphism from $\mathbf{A}$ to $\mathbf{B}$ is a function $h:A\rightarrow B$ that is a homomorphism: $h(x ... y)=h(x) ... h(y)$
 Let $\mathbf{A}$ and $\mathbf{B}$ be ... . A morphism from $\mathbf{A}$ to $\mathbf{B}$ is a function $h:A\rightarrow B$ that is an orderpreserving homomorphism: $h(x + y)=h(x) + h(y)$ and $x\le y\implies h(x)\le h(y)$.

Changed: 77c72
 Classtype & (value, see description) \cite{Ln19xx} \\\hline
 Classtype & universal \\\hline