# Differences

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

complete_distributive_lattices [2010/07/29 15:46] (current)
Line 1: Line 1:
+=====Complete distributive lattices=====
+
+Abbreviation: **CDLat**
+
+====Definition====
+A \emph{complete distributive lattice} is a [[complete lattice]] $\mathbf{A}=\langle A,\bigvee,\bigwedge\rangle$ such that
+
+$\vee$ distributes over $\wedge$:  $x\vee (y\wedge z)=(x\vee y)\wedge(x\vee z)$
+
+Remark:
+Click on the 'Edit text of this page' link at the bottom to add some information about complete distributive lattices
+
+It is not unusual to give several (equivalent) definitions. Ideally, one of the definitions would give an irredundant axiomatization that does not refer to other classes.
+
+==Morphisms==
+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:
+$h(x ... y)=h(x) ... h(y)$
+
+====Definition====
+An \emph{...} is a structure $\mathbf{A}=\langle A,...\rangle$ of type $\langle +...\rangle$ such that
+
+$...$ is ...:  $axiom$
+
+$...$ is ...:  $axiom$
+
+====Examples====
+Example 1:
+
+====Basic results====
+
+
+====Properties====
+Feel free to add or delete properties from this list. The list below may contain properties that are not relevant to the class that is being described.
+
+^[[Classtype]]                        |second-order  |
+^[[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====
+
+====Subclasses====
+  [[...]] subvariety
+
+  [[...]] expansion
+
+
+====Superclasses====
+  [[...]] supervariety
+
+  [[...]] subreduct
+
+
+====References====
+
+%[(Ln19xx>
+%F. Lastname, \emph{Title}, Journal, \textbf{1}, 23--45 [[MRreview]]
+)]
+
+

##### Toolbox 