# Absorption and directed Jónsson terms

@article{Kazda2018AbsorptionAD, title={Absorption and directed J{\'o}nsson terms}, author={Alexandr Kazda and Marcin Kozik and Ralph McKenzie and Matthew Moore}, journal={arXiv: Rings and Algebras}, year={2018}, pages={203-220} }

We prove that every congruence distributive variety has directed Jonsson terms, and every congruence modular variety has directed Gumm terms. The directed terms we construct witness every case of absorption witnessed by the original Jonsson or Gumm terms. This result is equivalent to a pair of claims about absorption for admissible preorders in congruence distributive and congruence modular varieties, respectively. For finite algebras, these absorption theorems have already seen significant…

## 21 Citations

The Gumm level equals the alvin level in congruence distributive varieties

- Mathematics
- 2020

Congruence modular and congruence distributive varieties can be characterized by the existence of sequences of Gumm and Jónsson terms, respectively. Such sequences have variable lengths, in general.…

Day's Theorem is sharp for $n$ even

- Mathematics
- 2019

Both congruence distributive and congruence modular varieties admit Maltsev characterizations by means of the existence of a finite but variable number of appropriate terms. A. Day showed that from…

Mitschke’s theorem is sharp

- MathematicsAlgebra universalis
- 2022

Mitschke showed that a variety with an m -ary near-unanimity term has Jónsson terms $$t_0, \dots , t _{2m-4} $$ t 0 , ⋯ , t 2 m - 4 witnessing congruence distributivity. We show that Mitschke’s…

DECIDING SOME MALTSEV CONDITIONS IN FINITE IDEMPOTENT ALGEBRAS

- MathematicsThe Journal of Symbolic Logic
- 2020

It is shown that for such “path defined” Maltsev conditions, the decision problem is polynomial-time solvable.

THE DISTRIBUTIVITY SPECTRUM OF BAKER’S VARIETY

- MathematicsJournal of the Australian Mathematical Society
- 2020

Abstract For every n, we evaluate the smallest k such that the congruence inclusion
$\alpha (\beta \circ _n \gamma ) \subseteq \alpha \beta \circ _{k} \alpha \gamma $
holds in a variety of reducts…

MALTSEV CONDITIONS FOR GENERAL CONGRUENCE MEET-SEMIDISTRIBUTIVE ALGEBRAS

- MathematicsThe Journal of Symbolic Logic
- 2021

Abstract Meet semidistributive varieties are in a sense the last of the most important classes in universal algebra for which it is unknown whether it can be characterized by a strong Maltsev…

MALTSEV CONDITIONS FOR GENERAL CONGRUENCE MEET-SEMIDISTRIBUTIVE ALGEBRAS

- MathematicsThe Journal of Symbolic Logic
- 2021

Meet semidistributive varieties are in a sense the last of the most important classes in universal algebra for which it is unknown whether it can be characterized by a strong Maltsev condition. We…

Deciding absorption

- MathematicsInt. J. Algebra Comput.
- 2016

Infinite idempotent algebras are characterized by means of Jónsson absorption and cube term blockers and it is decidable whether a given subset is an absorbing subuniverse of an algebra given by the tables of its basic operations.

Satisfiability in multi-valued circuits

- Mathematics, Computer ScienceLICS
- 2018

This paper seems to be the first systematic study of the computational complexity of satisfiability of non-Boolean circuits and solving equations over finite algebras and characterization is given in terms of nice structural properties of algeBRas for which the problems are solvable in polynomial time.

M ay 2 01 8 Relation identities in implication algebras

- Mathematics
- 2018

Let α, β, γ, . . . Θ, Ψ, . . . R, S, T, . . . be variables for, respectively, congruences, tolerances and reflexive admissible relations. Let juxtaposition denote intersection. We show that the…

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