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varieties: 6 Hits
=== 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: 5 Hits
rties==== ^[[Classtype]] |variety | ^[[Equational theory]] |decidabl... classes==== [[Idempotent monounary algebras]] subvariety The variety of monounary algebras has countably ... 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 the variety of se
boolean_semilattices: 4 Hits
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
nonassociative_relation_algebras: 3 Hits
results==== ====Properties==== ^[[Classtype]] |variety | ^[[Equational theory]] |decidable | ^[[Quasieq... uationally def. pr. cong.]] | | ^[[Discriminator variety]] |no | ^[[Amalgamation property]] | | ^[[Stron
tense_algebras: 3 Hits
results==== ====Properties==== ^[[Classtype]] |variety | ^[[Equational theory]] |decidable | ^[[Quasieq... tionally def. pr. cong.]] |no | ^[[Discriminator variety]] |no | ^[[Amalgamation property]] |yes | ^[[St
relation_algebras: 3 Hits
results==== ====Properties==== ^[[Classtype]] |variety | ^[[Equational theory]] |undecidable | ^[[Quasi... ionally def. pr. cong.]] |yes | ^[[Discriminator variety]] |yes | ^[[Amalgamation property]] |no | ^[[St
normal_valued_lattice-ordered_groups: 3 Hits
e$ ====Examples==== ====Basic results==== The variety of normal valued $\ell$-groups is the largest proper subvariety of [[lattice-ordered groups]] [(Holland1976)]. ====Properties==== ^[[Classtype]] |variety | ^[[Equational theory]] | | ^[[Quasiequational theory]] ... 976> W. Charles Holland, \emph{The largest proper variety of lattice-ordered groups}, Proceedings of the AM
sequential_algebras: 3 Hits
results==== ====Properties==== ^[[Classtype]] |variety | ^[[Equational theory]] |undecidable | ^[[Quasi... ionally def. pr. cong.]] |yes | ^[[Discriminator variety]] |no | ^[[Amalgamation property]] |no | ^[[Str
closure_algebras: 3 Hits
results==== ====Properties==== ^[[Classtype]] |variety | ^[[Equational theory]] |decidable | ^[[Quasieq... ionally def. pr. cong.]] |yes | ^[[Discriminator variety]] |no | ^[[Amalgamation property]] |yes | ^[[St
boolean_semigroups: 3 Hits
results==== ====Properties==== ^[[Classtype]] |variety | ^[[Equational theory]] | | ^[[Quasiequational ... ay}$ ====Subclasses==== [[Boolean monoids]] [[Variety generated by complex algebras of semigroups]] =
modal_algebras: 3 Hits
results==== ====Properties==== ^[[Classtype]] |variety | ^[[Equational theory]] |decidable | ^[[Quasieq... tionally def. pr. cong.]] |no | ^[[Discriminator variety]] |no | ^[[Amalgamation property]] |yes | ^[[St
equationally_def._pr._cong: 3 Hits
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
hilbert_algebras: 2 Hits
(\to,1)$-subreducts of [[Heyting algebras]]. The variety of Hilbert algebras is not generated as a quasivariety by any of its finite members [(CelaniCabrer2005)]. ====Properties==== ^[[Classtype]] |variety [(Diego1966)] | ^[[Equational theory]] | | ^[[Quasiequation... &\\ \end{array}$ ====Subclasses==== [[...]] subvariety [[...]] expansion ====Superclasses==== [[...]]
abelian_groups: 2 Hits
, with addition, unary subtraction, and zero. The variety of abelian groups is generated by this algebra. ... perties==== ^[[Classtype]] |variety | ^[[Equational theory]] |decidable
lattices: 2 Hits
hoops: 2 Hits
right_hoops: 2 Hits
semilattices: 2 Hits
bilattices: 1 Hits
groups: 1 Hits
bck-lattices: 1 Hits
semirings: 1 Hits
fl-algebras: 1 Hits
categories: 1 Hits
m-zeroid: 1 Hits
loops: 1 Hits
bck-algebras: 1 Hits
semigroups: 1 Hits
quandles: 1 Hits
mv-algebras: 1 Hits
rings: 1 Hits
near-rings: 1 Hits
normal_bands: 1 Hits
quasigroups: 1 Hits
monoids: 1 Hits
binars: 1 Hits
classtype: 1 Hits
sets: 1 Hits
shells: 1 Hits
fle-algebras: 1 Hits
m-sets: 1 Hits
bands: 1 Hits
properties: 1 Hits
lie_algebras: 1 Hits
directoids: 1 Hits