# Differences

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

relation_algebras [2010/07/29 15:46]
127.0.0.1 external edit
relation_algebras [2010/09/17 20:45] (current)
jipsen
Line 24: Line 24:
====Examples==== ====Examples====
-Example 1: +Example 1: $\langle \mathcal P(U^2), \cup, \emptyset, \cap, U^2, -, \circ, ^\smile, id_U \rangle$ the full relation algebra of binary relations on a set $U$.
+
+Example 2: $\langle \mathcal P(G), \cup, \emptyset, \cap, G, -, \circ, ^\smile, \{e\} \rangle$ the group relation algebra of a [[group]] $\langle G, *, ^{-1}, e \rangle$, where $X\circ Y=\{x*y : x\in X, y\in Y\}$ and $X^\smile=\{x^{-1} : x\in X\}$.
====Basic results==== ====Basic results====
Line 48: Line 50:
^[[Strong amalgamation property]]  |no | ^[[Strong amalgamation property]]  |no |
^[[Epimorphisms are surjective]]  |no | ^[[Epimorphisms are surjective]]  |no |
+
+
====Finite members==== ====Finite members====
$\begin{array}{lr}$\begin{array}{lr}
-[http://localhost/gap/ramaddux.html Small relation algebras]
-
f(1)= &1\\ f(1)= &1\\
f(2)= &1\\ f(2)= &1\\
Line 60: Line 62:
f(6)= &0\\ f(6)= &0\\
\end{array}$\end{array}$
+
+[[http://www.chapman.edu/~jipsen/gap/ramaddux.html|Small relation algebras]]
+
====Subclasses==== ====Subclasses====
Line 69: Line 74:
[[Square-increasing relation algebras]] [[Square-increasing relation algebras]]
+
====Superclasses==== ====Superclasses====
Line 78: Line 84:
====References==== ====References====
-[(Ln19xx> +/*[(Ln19xx> )]*/
-)] +
- +
- +
- +
- +