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
- modal_algebras
- results==== ====Properties==== ^[[Classtype]] |variety | ^[[Equational theory]] |decidable | ^[[Quasieq... tionally def. pr. cong.]] |no | ^[[Discriminator variety]] |no | ^[[Amalgamation property]] |yes | ^[[St
- kleene_logic_algebras
- sults==== The algebra in Example 1 generates the variety of Kleene logic algebras ====Properties==== ^[[Classtype]] |Variety | ^[[Equational theory]] |Decidable | ^[[Quasieq
- hoops
- Remark: This definition shows that hoops form a variety. Hoops are partially ordered by the relation $x\... nd integral. ====Properties==== ^[[Classtype]] |variety | ^[[Equational theory]] |decidable | ^[[Quasieq
- relation_algebras
- results==== ====Properties==== ^[[Classtype]] |variety | ^[[Equational theory]] |undecidable | ^[[Quasi... ionally def. pr. cong.]] |yes | ^[[Discriminator variety]] |yes | ^[[Amalgamation property]] |no | ^[[St
- sqrt-quasi-mv-algebras
- ac12,\frac12\rangle$. ====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
