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+ | =====Conjugative binars===== | ||
+ | |||
+ | Abbreviation: **ConBin** | ||
+ | ====Definition==== | ||
+ | A \emph{conjugative binar} is a [[binar]] $\mathbf{A}=\langle A,\cdot\rangle$ such that | ||
+ | |||
+ | $\cdot$ is conjugative: $\exists w, \ x\cdot w=y \iff \exists w, \ w\cdot x=y$. | ||
+ | |||
+ | ==Morphisms== | ||
+ | Let $\mathbf{A}$ and $\mathbf{B}$ be commutative binars. A morphism from $\mathbf{A}$ to $\mathbf{B}$ is a function $h:A\rightarrow B$ that is a homomorphism: | ||
+ | |||
+ | $h(x\cdot y)=h(x)\cdot h(y)$ | ||
+ | |||
+ | ====Examples==== | ||
+ | Example 1: | ||
+ | |||
+ | ====Basic results==== | ||
+ | |||
+ | |||
+ | ====Properties==== | ||
+ | ^[[Classtype]] | first-order | | ||
+ | ^[[Equational theory]] | | | ||
+ | ^[[Quasiequational theory]] | | | ||
+ | ^[[First-order theory]] | | | ||
+ | ^[[Locally finite]] | no | | ||
+ | ^[[Residual size]] | | | ||
+ | ^[[Congruence distributive]] | no | | ||
+ | ^[[Congruence modular]] | no | | ||
+ | ^[[Congruence n-permutable]] | no | | ||
+ | ^[[Congruence regular]] | no | | ||
+ | ^[[Congruence uniform]] | no | | ||
+ | ^[[Congruence extension property]] | | | ||
+ | ^[[Definable principal congruences]] | | | ||
+ | ^[[Equationally def. pr. cong.]] | | | ||
+ | ^[[Amalgamation property]] | | | ||
+ | ^[[Strong amalgamation property]] | | | ||
+ | ^[[Epimorphisms are surjective]] | | | ||
+ | |||
+ | ====Finite members==== | ||
+ | |||
+ | ^n ^ # of algebras^ | ||
+ | |1 | 1| | ||
+ | |2 | 4| | ||
+ | |3 | 215| | ||
+ | |||
+ | ====Subclasses==== | ||
+ | [[Commutative binars]] | ||
+ | |||
+ | [[Conjugative semigroups]] | ||
+ | |||
+ | ====Superclasses==== | ||
+ | [[Binars]] | ||
+ | |||
+ | ====References==== | ||
+ | |||
+ | |||
+ | |||
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