Differences

—		distributive_p-algebras [2010/07/29 15:46] (current)
Line 1:		Line 1:
		+	=====Distributive p-algebras=====
		+	Abbreviation: **DpAlg**
		+	====Definition====
		+	A \emph{distributive p-algebra} is a structure $\mathbf{L}=\langle L,\vee ,0,\wedge ,1,^*\rangle $ such that
		+
		+
		+	$\langle L,\vee,0,\wedge,1\rangle $ is a [[bounded distributive lattices]]
		+
		+
		+	$x^*$ is the \emph{pseudo complement} of $x$:  $y\leq x^* \iff x\wedge y=0$
		+
		+	==Morphisms==
		+	Let $\mathbf{L}$ and $\mathbf{M}$ be distributive p-algebras. A morphism from $\mathbf{L}$ to $\mathbf{M}$ is a function $h:L\rightarrow M$ that is a
		+	homomorphism:
		+
		+	$h(x\vee y)=h(x)\vee h(y)$, $h(x\wedge y)=h(x)\wedge h(y)$, $h(0)=0 $, $h(1)=1$, $h(x^*)=h(x)^*$
		+
		+	====Examples====
		+	Example 1:
		+
		+	====Basic results====
		+
		+	====Properties====
		+	^[[Classtype]]  |variety |
		+	^[[Equational theory]]  |decidable |
		+	^[[Quasiequational theory]]  | |
		+	^[[First-order theory]]  | |
		+	^[[Congruence distributive]]  |yes |
		+	^[[Congruence modular]]  |yes |
		+	^[[Congruence n-permutable]]  | |
		+	^[[Congruence regular]]  | |
		+	^[[Congruence uniform]]  | |
		+	^[[Congruence extension property]]  | |
		+	^[[Definable principal congruences]]  | |
		+	^[[Equationally def. pr. cong.]]  | |
		+	^[[Amalgamation property]]  |yes |
		+	^[[Strong amalgamation property]]  | |
		+	^[[Epimorphisms are surjective]]  | |
		+	^[[Locally finite]]  | |
		+	^[[Residual size]]  | |
		+	====Finite members====
		+
		+	$\begin{array}{lr}
		+	f(1)= &1\\
		+	f(2)= &1\\
		+	f(3)= &1\\
		+	f(4)= &\\
		+	f(5)= &\\
		+	f(6)= &\\
		+	f(7)= &\\
		+	\end{array}$
		+
		+	====Subclasses====
		+	[[Distributive double p-algebras]]
		+
		+	====Superclasses====
		+	[[Distributive lattices]]
		+
		+
		+	====References====
		+
		+	[(Ln19xx>
		+	)]