# Differences

This shows you the differences between two versions of the page.

integral_ordered_monoids [2016/11/26 18:44] (current)
jipsen created
Line 1: Line 1:
+=====Integral ordered monoids=====
+
+Abbreviation: **IOMon**
+
+====Definition====
+An \emph{integral ordered monoid} is a [[ordered monoid]] $\mathbf{A}=\langle A,\cdot,1,\le\rangle$ that is
+
+\emph{integral}:  $x\le 1$
+
+
+==Morphisms==
+Let $\mathbf{A}$ and $\mathbf{B}$ be ordered monoids. A morphism from $\mathbf{A}$ to $\mathbf{B}$ is a function $h:A\rightarrow B$ that is a orderpreserving homomorphism:
+$h(x \cdot y)=h(x) \cdot h(y)$,
+$h(1)=1$,
+$x\le y\Longrightarrow h(x)\le h(y)$.
+
+
+====Examples====
+Example 1:
+
+====Basic results====
+
+
+====Properties====
+
+^[[Classtype]]                        |universal  |
+^[[Equational theory]]                | |
+^[[Quasiequational theory]]           | |
+^[[First-order theory]]               | |
+^[[Locally finite]]                   | |
+^[[Residual size]]                    | |
+^[[Congruence distributive]]          | |
+^[[Congruence modular]]               | |
+^[[Congruence $n$-permutable]]        | |
+^[[Congruence regular]]               | |
+^[[Congruence uniform]]               | |
+^[[Congruence extension property]]    | |
+^[[Definable principal congruences]]  | |
+^[[Equationally def. pr. cong.]]      | |
+^[[Amalgamation property]]            | |
+^[[Strong amalgamation property]]     | |
+^[[Epimorphisms are surjective]]      | |
+
+====Finite members====
+$f(n)=$ number of members of size $n$.
+
+$\begin{array}{lr} +f(1)= &1\\ +f(2)= &1\\ +f(3)= &2\\ +f(4)= &8\\ +f(5)= &44\\ +f(6)= &308\\ +f(7)= &2641\\ +f(8)= &27120\\ +f(9)= &\\ +\end{array}$
+
+====Subclasses====
+[[Commutative integral ordered monoids]]
+
+
+====Superclasses====
+[[Ordered monoids]]
+
+
+====References====
+
+[(Lastname19xx>
+F. Lastname, \emph{Title}, Journal, \textbf{1}, 23--45 [[MRreview]]
+)]
+
+