Complexity of Quasivariety Lattices

Schwidefsky, M. V.

doi:10.1007/s10469-015-9344-7

Cited by 9 publications

(1 citation statement)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In [12] a sufficient condition for a class K to have continuum many subclasses with the property (N) but which are not Q-universal was established. In [13] it was proved that almost all known Q-universal quasivarieties contain classes having property (N).…”

Section: Discussionmentioning

confidence: 99%

On quasi-identities of finite modular lattices

Lutsak

Voronina

Nurakhmetova

2022

JMMCS

View full text Add to dashboard Cite

In 1970 R. McKenzie proved that any finite lattice has a finite basis of identities. However the similar result for quasi-identities is not true. That is, there is a finite lattice that has no finite basis of quasi-identities. The problem "Which finite lattices have finite bases of quasi-identities?" was suggested by V.A. Gorbunov and D.M. Smirnov. In 1984 V.I. Tumanov found a sufficient condition consisting of two parts under which a locally finite quasivariety of lattices has no finite (independent) basis of quasi-identities. Also he conjectured that a finite (modular) lattice has a finite basis of quasi-identities if and only if a quasivariety generated by this lattice is a variety. In general, the conjecture is not true. W. Dziobiak found a finite lattice that generates a finitely axiomatizable proper quasivariety. Tumanov's problem is still unsolved for modular lattices. We construct a finite modular lattice that does not satisfy one of Tumanov's conditions but the quasivariety generated by this lattice is not finitely based.

show abstract

Section: Discussionmentioning

confidence: 99%

On quasi-identities of finite modular lattices

Lutsak

Voronina

Nurakhmetova

2022

JMMCS

View full text Add to dashboard Cite

show abstract

Introduction

Adaricheva

Hyndman

Nation

et al. 2022

CMS/CAIMS Books in Mathematics

View full text Add to dashboard Cite

The Lattice of Subquasivarieties of a Locally Finite Quasivariety

Hyndman¹,

Nation²

2018

CMS Books in Mathematics

View full text Add to dashboard Cite

the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

show abstract

Complexity of Quasivariety Lattices

Cited by 9 publications

References 26 publications

On quasi-identities of finite modular lattices

On quasi-identities of finite modular lattices

Introduction

The Lattice of Subquasivarieties of a Locally Finite Quasivariety

Contact Info

Product

Resources

About