# Residually finite, congruence meet-semidistributive varieties of finite type have a finite residual bound

@inproceedings{Willard1999ResiduallyFC, title={Residually finite, congruence meet-semidistributive varieties of finite type have a finite residual bound}, author={R. Willard and K. Kearnes}, year={1999} }

We show that a residually finite, congruence meet-semidistributive variety of finite type is residually < N for some finite N . This solves Pixley’s problem and a special case of the restricted Quackenbush problem.

#### 22 Citations

A finite basis theorem for residually finite, congruence meet-semidistributive varieties

- Mathematics, Computer Science
- Journal of Symbolic Logic
- 2000

A Mal'cev condition for congruence meet-semidistributivity is derived and used to prove two theorems: if a variety in a finite language is congruent and residually less than some finite cardinal, then it is finitely based. Expand

Optimal strong Mal’cev conditions for congruence meet-semidistributivity in locally finite varieties

- Mathematics
- 2016

Locally finite, congruence meet-semidistributive varieties have been characterized by numerous Mal’cev conditions and, recently, by two strong Mal’cev conditions. We provide three new strong Mal’cev… Expand

Residually Finite Varieties of Nonassociative Algebras

- Mathematics
- 2010

We prove that if 𝒱 is a residually finite variety of nonassociative algebras over a finite field, and the enveloping algebra of each finite member of 𝒱 is finitely generated as a module over its… Expand

A characterization of idempotent strong Mal’cev conditions for congruence meet-semidistributivity in locally finite varieties

- Mathematics
- 2018

We prove a characterization of all idempotent, linear, strong Mal’cev conditions in two variables which hold in all locally finite congruence meet-semidistributive varieties. This is an alternative… Expand

Extending Baker's theorem

- Mathematics
- 2001

Abstract. We summarize the combinatorial properties of congruence generation in congruence distributive varieties which are relevant to Baker's finite basis theorem, explain the extent to which these… Expand

On profinite completions and canonical extensions

- Mathematics
- 2006

Abstract.We show that if a variety V of monotone lattice expansions is finitely generated, then profinite completions agree with canonical extensions on V. The converse holds for varieties of finite… Expand

A quasi-Mal’cev condition with unexpected application

- Mathematics
- 2015

A quasi-Mal’cev condition for quasivarieties is established which in the case of locally finite quasivarieties forbids strongly abelian congruences and for varieties is equivalent to possessing a… Expand

On strong Mal'cev conditions for congruence meet-semidistributivity in a locally finite variety

- Mathematics
- 2014

In this paper we examine four-element and five-element digraphs for existence of certain polymorphisms that imply congruence meet-semidistributivity in a locally finite variety. The results presented… Expand

On the semidistributivity of elements in weak congruence lattices of algebras and groups

- Mathematics
- 2008

Abstract.Weak congruence lattices and semidistributive congruence lattices are both recent topics in universal algebra. This motivates the main result of the present paper, which asserts that a… Expand

ON OPTIMAL STRONGMAL ’ CEV CONDITIONS FOR CONGRUENCE MEET – SEMIDISTRIBUTIVITY IN A LOCALLY FINITE VARIETY

- 2014

In this paper we examine four–element and five–element digraphs for existence of certain polymorphisms that imply congruence meet–semidistributivity in a locally finite variety. The results presented… Expand

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