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—		rectangular_bands [2010/07/29 15:46] (current)
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		+	=====Rectangular bands=====
		+	Abbreviation: **RBand**
		+	====Definition====
		+	A \emph{rectangular band} is a [[bands]] $\mathbf{B}=\langle B,\cdot
		+	\rangle $ such that
		+
		+	$\cdot $ is rectangular:  $x\cdot y\cdot x=x$.
		+	====Definition====
		+	A \emph{rectangular band} is a [[bands]] $\mathbf{B}=\langle B,\cdot
		+	\rangle $ such that
		+
		+	$x\cdot y\cdot z=x\cdot z$.
		+	==Morphisms==
		+	Let $\mathbf{B}$ and $\mathbf{C}$ be rectangular 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====
		+	[[Left-zero semigroups]]
		+
		+	[[Right-zero semigroups]]
		+
		+	====Superclasses====
		+	[[Normal bands]]
		+
		+
		+	====References====
		+
		+	[(Ln19xx>
		+	)]