# Finitely generated almost universal varieties of $0$-lattices

Commentationes Mathematicae Universitatis Carolinae (2005)

- Volume: 46, Issue: 2, page 301-325
- ISSN: 0010-2628

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topKoubek, Václav, and Sichler, Jiří. "Finitely generated almost universal varieties of $0$-lattices." Commentationes Mathematicae Universitatis Carolinae 46.2 (2005): 301-325. <http://eudml.org/doc/22822>.

@article{Koubek2005,

abstract = {A concrete category $\mathbb \{K\}$ is (algebraically) universal if any category of algebras has a full embedding into $\mathbb \{K\}$, and $\mathbb \{K\}$ is almost universal if there is a class $\mathcal \{C\}$ of $\mathbb \{K\}$-objects such that all non-constant homomorphisms between them form a universal category. The main result of this paper fully characterizes the finitely generated varieties of $0$-lattices which are almost universal.},

author = {Koubek, Václav, Sichler, Jiří},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {(algebraically) universal category; finite-to-finite universal category; almost universal category; $0$-lattice; variety of $0$-lattices; algebraic system; variety; -universal quasivariety; categorical universality},

language = {eng},

number = {2},

pages = {301-325},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {Finitely generated almost universal varieties of $0$-lattices},

url = {http://eudml.org/doc/22822},

volume = {46},

year = {2005},

}

TY - JOUR

AU - Koubek, Václav

AU - Sichler, Jiří

TI - Finitely generated almost universal varieties of $0$-lattices

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 2005

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 46

IS - 2

SP - 301

EP - 325

AB - A concrete category $\mathbb {K}$ is (algebraically) universal if any category of algebras has a full embedding into $\mathbb {K}$, and $\mathbb {K}$ is almost universal if there is a class $\mathcal {C}$ of $\mathbb {K}$-objects such that all non-constant homomorphisms between them form a universal category. The main result of this paper fully characterizes the finitely generated varieties of $0$-lattices which are almost universal.

LA - eng

KW - (algebraically) universal category; finite-to-finite universal category; almost universal category; $0$-lattice; variety of $0$-lattices; algebraic system; variety; -universal quasivariety; categorical universality

UR - http://eudml.org/doc/22822

ER -

## References

top- Adams M.E., Dziobiak W., Finite-to-finite universal quasivarieties are $Q$-universal, Algebra Universalis 46 (2001), 253-283. (2001) Zbl1059.08002MR1835799
- Dziobiak W., On lattice identities satisfied in subquasivariety lattices of varieties of modular lattices, Algebra Universalis 22 (1986), 205-214. (1986) Zbl0608.06005MR0870468
- Goralčík P., Koubek V., Sichler J., Universal varieties of (0,1)-lattices, Canad. Math. J. 42 (1990), 470-490. (1990) Zbl0709.18003MR1062740
- Grätzer G., Sichler J., On the endomorphism semigroup (and category) of bounded lattices, Pacific J. Math. 35 (1970), 639-647. (1970) MR0277442
- Koubek V., Sichler J., Universal varieties of semigroups, J. Austral. Math. Soc. (Series A) 36 (1984),143-152. (1984) Zbl0549.20038MR0725742
- Koubek V., Sichler J., Almost universal varieties of monoids, Algebra Universalis 19 (1984), 330-334. (1984) Zbl0551.20047MR0779149
- Koubek V., Sichler J., Universality of small lattice varieties, Proc. Amer. Math. Soc. 91 (1984), 19-24. (1984) Zbl0507.06006MR0735556
- Koubek V., Sichler J., On almost universal varieties of modular lattices, Algebra Universalis 45 (2001), 191-210. (2001) Zbl0981.06004MR1810548
- Koubek V., Sichler J., On relative universality and $Q$-universality, Studia Logica 78 (2004), 279-291. (2004) Zbl1079.08009MR2108030
- Koubek V., Sichler J., Almost $ff$-universal and $Q$-universal varieties of modular $0$-lattices, Colloq. Math., to appear. Zbl1066.06004MR2110722
- McKenzie R., Tsinakis C., On recovering bounded distributive lattice from its endomorphism monoid, Houston J. Math. 7 (1981), 525-529. (1981) MR0658568
- Pultr A., Trnková V., Combinatorial, algebraic and topological representations of groups, semigroups and categories, North Holland Amsterdam (1980). (1980) MR0563525
- Ribenboim P., Characterization of the sup-complement in a distributive lattice with last element, Summa Brasil Math. 2 (1949), 43-49. (1949) Zbl0040.01003MR0030931
- Sapir M.V., The lattice of quasivarieties of semigroups, Algebra Universalis 21 (1985), 172-180. (1985) Zbl0599.08014MR0855737

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