Almost ff-universal and q-universal varieties of modular 0-lattices

V. Koubek, and J. Sichler. "Almost ff-universal and q-universal varieties of modular 0-lattices." Colloquium Mathematicae 101.2 (2004): 161-182. <http://eudml.org/doc/284258>.

@article{V2004,
abstract = {A variety 𝕍 of algebras of a finite type is almost ff-universal if there is a finiteness-preserving faithful functor F: 𝔾 → 𝕍 from the category 𝔾 of all graphs and their compatible maps such that Fγ is nonconstant for every γ and every nonconstant homomorphism h: FG → FG' has the form h = Fγ for some γ: G → G'. A variety 𝕍 is Q-universal if its lattice of subquasivarieties has the lattice of subquasivarieties of any quasivariety of algebras of a finite type as the quotient of its sublattice. For a variety 𝕍 of modular 0-lattices it is shown that 𝕍 is almost ff-universal if and only if 𝕍 is Q-universal, and that this is also equivalent to the non-distributivity of 𝕍.},
author = {V. Koubek, J. Sichler},
journal = {Colloquium Mathematicae},
keywords = {modular lattice; variety; quasivariety; -universality; -universality; finite-to-finite universal category},
language = {eng},
number = {2},
pages = {161-182},
title = {Almost ff-universal and q-universal varieties of modular 0-lattices},
url = {http://eudml.org/doc/284258},
volume = {101},
year = {2004},
}

TY - JOUR
AU - V. Koubek
AU - J. Sichler
TI - Almost ff-universal and q-universal varieties of modular 0-lattices
JO - Colloquium Mathematicae
PY - 2004
VL - 101
IS - 2
SP - 161
EP - 182
AB - A variety 𝕍 of algebras of a finite type is almost ff-universal if there is a finiteness-preserving faithful functor F: 𝔾 → 𝕍 from the category 𝔾 of all graphs and their compatible maps such that Fγ is nonconstant for every γ and every nonconstant homomorphism h: FG → FG' has the form h = Fγ for some γ: G → G'. A variety 𝕍 is Q-universal if its lattice of subquasivarieties has the lattice of subquasivarieties of any quasivariety of algebras of a finite type as the quotient of its sublattice. For a variety 𝕍 of modular 0-lattices it is shown that 𝕍 is almost ff-universal if and only if 𝕍 is Q-universal, and that this is also equivalent to the non-distributivity of 𝕍.
LA - eng
KW - modular lattice; variety; quasivariety; -universality; -universality; finite-to-finite universal category
UR - http://eudml.org/doc/284258
ER -