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conjugative_binars [2018/08/04 18:39] (current)
jipsen created
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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====
 +
 +
 +