Mathematical Structures: History of Lattice-ordered monoids

History of Lattice-ordered monoids

Difference (from prior major revision) (author diff)

Changed: 34c34

A lattice-ordered monoid (or $\ell$-monoid) is a structure $\mathbf{A}=\langle A,\vee,\wedge,\cdot,1\rangle$ of type $\langle 2,2,2,0\rangle$ such that

A lattice-ordered monoid (or $\ell$-monoid) is a structure $\mathbf{A}=\langle A\vee,\wedge,\cdot,1\rangle$ of type $\langle 2,2,2,0\rangle$ such that

Changed: 38c38

$\langle A,\cdot,1\rangle$ is a \href{Monoids.pdf}{monoids}

$\langle A,\cdot,1\rangle$ is a \href{Monoids.pdf}{monoid}

Changed: 49,50c49,53

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 lattice ordered monoids. A morphism from $\mathbf{A}$ to $\mathbf{B}$ is a function $h:A\rightarrow B$ that is a homomorphism:
$h(x \vee y)=h(x) \vee h(y)$,
$h(x \wedge y)=h(x) \wedge h(y)$,
$h(x \cdot y)=h(x) \cdot h(y)$,
$h(1)=1$.

Removed: 53,61d55

\begin{definition}
A ... is a structure $\mathbf{A}=\langle A,...\rangle$ of type $\langle
...\rangle$ such that

$...$ is ...: $axiom$

$...$ is ...: $axiom$
\end{definition}

Changed: 101,102c95,96

f(2)= &\\
f(3)= &\\

f(2)= &2\\
f(3)= &8\\

	Revision 4 . . July 19, 2005 8:45 pm by Jipsen
	Revision 3 . . July 19, 2005 8:41 pm by Jipsen
	Revision 2 . . July 30, 2004 12:36 pm by Jipsen
	Revision 1 . . July 29, 2004 12:25 pm by Jipsen