## Fulltext results:

- varieties
- === Varieties of universal algebras ===
A \emph{
**variety**} is a class of structures of the same signature th... 4, 1935)] a class $\mathcal{K}$ of algebras is a**variety**iff it is closed under the operators $H$, $S$, $P... $\mathcal{K}\}$. Equivalently, $\mathcal K$ is a**variety**iff $\mathcal K=HSP\mathcal K$. In particular, g... bras, $V\mathcal K=HSP\mathcal K$ is the smallest**variety**that contains $\mathcal K$, and is called the \em - monounary_algebras
- rties====
^[[Classtype]] |
**variety**| ^[[Equational theory]] |decidabl... [[Idempotent monounary algebras]] subvariety The**variety**of monounary algebras has countably many subvarie... ttice of divisibility of the natural numbers. The**variety**$\text{Mod}(x=y)$ of trivial subvarieties is the unique element below the**variety**$\text{Mod}(f(x)=x)$ (which is term-equivalent to - boolean_semilattices
- g,\cdot\rangle$ such that
$\mathbf{A}$ is in the
**variety**generated by complex algebras of semilattices Le... results==== ====Properties==== ^[[Classtype]] |**variety**| ^[[Finitely axiomatizable]] |open | ^[[Equatio... [[Some members of BSlat]] ====Subclasses==== [[**Variety**generated by complex algebras of linear semilatti - semilattices
- :
This definition shows that semilattices form a
**variety**. ==Morphisms== Let $\mathbf{S}$ and $\mathbf{T}$... shows that semilattices form a partially-ordered**variety**. ====Definition==== A \emph{join-semilattice} is ... results==== ====Properties==== ^[[Classtype]] |**variety**| ^[[Equational theory]] |decidable in polynomia - normal_valued_lattice-ordered_groups
- e$
====Examples====
====Basic results====
The
**variety**of normal valued $\ell$-groups is the largest pro... perties==== ^[[Classtype]] |**variety**| ^[[Equational theory]] | | ^[[Qua... 976> W. Charles Holland, \emph{The largest proper**variety**of lattice-ordered groups}, Proceedings of the AM - right_hoops
- k:
This definition shows that right hoops form a
**variety**. Right hoops are partially ordered by the relati... results==== ====Properties==== ^[[Classtype]] |**variety**| ^[[Equational theory]] | | ^[[Quasiequational - kleene_logic_algebras
- sults====
The algebra in Example 1 generates the
**variety**of Kleene logic algebras ====Properties==== ^[[Classtype]] |**Variety**| ^[[Equational theory]] |Decidable | ^[[Quasieq - modal_algebras
- results====
====Properties====
^[[Classtype]] |
**variety**| ^[[Equational theory]] |decidable | ^[[Quasieq... tionally def. pr. cong.]] |no | ^[[Discriminator**variety**]] |no | ^[[Amalgamation property]] |yes | ^[[St - equationally_def._pr._cong
- ly definable principal congruences=====
A (quasi)
**variety**$\mathcal{K}$ of algebraic structures has \emph{e... roperties that imply EDP(R)C === [[Discriminator**variety**]] === Properties implied by EDP(R)C === Relativ - sqrt-quasi-mv-algebras
- ac12,\frac12\rangle$.
====Basic results====
The
**variety**of $\sqrt{'}$qMV-algebras is generated by the sta... -algebra]]. ====Properties==== ^[[Classtype]] |**variety**| ^[[Equational theory]] |decidable | ^[[Quasieq - abelian_groups
- , with addition, unary subtraction, and zero. The
**variety**of abelian groups is generated by this algebra. ... perties==== ^[[Classtype]] |**variety**| ^[[Equational theory]] |decidable - congruence_n-permutable
- aracterized by a Mal'cev condition.
For $n=2$, a
**variety**is congruence permutable iff there exists a term ... the identities $p(x,z,z)=x=p(z,z,x)$ hold in the**variety**. === Properties that imply congruence $n$-permut - tense_algebras
- results====
====Properties====
^[[Classtype]] |
**variety**| ^[[Equational theory]] |decidable | ^[[Quasieq... tionally def. pr. cong.]] |no | ^[[Discriminator**variety**]] |no | ^[[Amalgamation property]] |yes | ^[[St - function_rings
- y)$.
====Examples====
====Basic results====
The
**variety**of $f$-rings is generated by the class of linearl... ory, 1967]). ====Properties==== ^[[Classtype]] |**variety**| ^[[Equational theory]] | | ^[[Quasiequational - sequential_algebras
- results====
====Properties====
^[[Classtype]] |
**variety**| ^[[Equational theory]] |undecidable | ^[[Quasi... ionally def. pr. cong.]] |yes | ^[[Discriminator**variety**]] |no | ^[[Amalgamation property]] |no | ^[[Str