Mathematical Structures: History of Abelian ordered groups

History of Abelian ordered groups

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

Changed: 28,29c28,29

\Large Name of class
\quad\href{http://math.chapman.edu/cgi-bin/structures?action=edit;id=Template}{edit}

\Large Abelian ordered groups
\quad\href{http://math.chapman.edu/cgi-bin/structures?action=edit;id=Abelian_ordered_groups}{edit}

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

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