# Differences

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normal_bands [2010/07/29 15:46] (current)
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+=====Normal bands=====
+Abbreviation: **NBand**
+====Definition====
+A \emph{normal band} is a [[bands]] $\mathbf{B}=\langle B,\cdot +\rangle$ such that
+
+$\cdot$ is normal:  $x\cdot y\cdot z\cdot x=x\cdot z\cdot y\cdot x$.
+==Morphisms==
+Let $\mathbf{B}$ and $\mathbf{C}$ be normal bands. A morphism from $\mathbf{B}$
+to $\mathbf{C}$ is a function $h:B\rightarrow C$ that is a homomorphism:
+
+$h(xy)=h(x)h(y)$
+
+====Examples====
+
+
+====Basic results====
+
+====Properties====
+^[[Classtype]]  |variety |
+^[[Equational theory]]  |decidable in polynomial time |
+^[[Quasiequational theory]]  | |
+^[[First-order theory]]  | |
+^[[Locally finite]]  |yes |
+^[[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====
+
+$\begin{array}{lr} +f(1)= &1\\ +f(2)= &\\ +f(3)= &\\ +f(4)= &\\ +f(5)= &\\ +f(6)= &\\ +f(7)= &\\ +\end{array}$
+
+====Subclasses====
+[[Rectangular bands]]
+
+====Superclasses====
+[[Bands]]
+
+
+====References====
+
+[(Ln19xx>
+)]