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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>
 +)]