# Independence of algebras with edge term

@article{Aichinger2015IndependenceOA, title={Independence of algebras with edge term}, author={Erhard Aichinger and Peter Mayr}, journal={Int. J. Algebra Comput.}, year={2015}, volume={25}, pages={1145-1157} }

Two varieties $V, W$ of the same type are independent if there is a binary term $t(x,y)$ such that $V \models t(x,y) \approx x$ and $W \models t(x,y) \approx y$. In this note, we give necessary and sufficient conditions for two finite algebras with a Mal'cev term (or, more generally, with an edge term) to generate independent varieties. In particular we show that the independence of finitely generated varieties with edge term can be decided by a polynomial time algorithm.

## 4 Citations

### Congruence preserving expansions of nilpotent algebras

- MathematicsInt. J. Algebra Comput.
- 2020

Those nilpotent algebras of prime power order and finite type in congruence modular varieties that have infinitely many polynomially inequivalent congruent expansions are characterized.

### Expansions of abelian squarefree groups.

- Mathematics
- 2020

We investigate finitary functions from $\mathbb{Z}_{n}$ to $\mathbb{Z}_{n}$ for a squarefree number $n$. We show that the lattice of all clones on the squarefree set $\mathbb{Z}_{p_1\cdots p_m}$…

### Clones containing the Mal'cev operation of $\mathbb{Z}_{pq}$

- Mathematics
- 2020

We investigate finitary functions from $\mathbb{Z}_{pq}$ to $\mathbb{Z}_{pq}$ for two distinct prime numbers $p$ and $q$. We show that the lattice of all clones on the set $\mathbb{Z}_{pq}$ which…

### Between an n-ary and an n + 1-ary near-unanimity term

- GeologyInternational Journal of Algebra and Computation
- 2022

We devise a condition strictly between the existence of an [Formula: see text]-ary and an [Formula: see text]-ary near-unanimity term. We evaluate exactly the distributivity and modularity levels…

## References

SHOWING 1-10 OF 13 REFERENCES

### On independent varieties and some related notions

- Mathematics
- 2013

We investigate the relation of independence between varieties, as well as a generalisation of such which we call strict quasi-independence. Concerning the former notion, we specify a procedure for…

### ON NEAR-RING IDEMPOTENTS AND POLYNOMIALS ON DIRECT PRODUCTS OF Ω-GROUPS

- MathematicsProceedings of the Edinburgh Mathematical Society
- 2001

Abstract Let $N$ be a zero-symmetric near-ring with identity, and let $\sGa$ be a faithful tame $N$-group. We characterize those ideals of $\sGa$ that are the range of some idempotent element of $N$.…

### Clones of Algebras with Parallelogram Terms

- MathematicsInt. J. Algebra Comput.
- 2012

A manageable set of relations is described that generates the finitary relational clone of an algebra with a parallelogram term which generates residually small varieties on any finite set and for any finite k there are only finitely many clones of algebras with a k-ary paralle Logram term.

### Varieties with few subalgebras of powers

- Mathematics
- 2009

The Constraint Satisfaction Problem Dichotomy Conjecture of Feder and Vardi (1999) has in the last 10 years been profitably reformulated as a conjecture about the set SP fin (A) of subalgebras of…

### Joins and Direct Products of Equational Classes

- MathematicsCanadian Mathematical Bulletin
- 1969

Let K0 and K1 be equational classes of algebras of the same type. The smallest equational class K containing K0 and K1 is the join of K0 and K1; in notation, K = K0 ∨ K1. The direct product K0 × K1…

### Products of Classes of Residuated Structures

- MathematicsStud Logica
- 2004

The central result of this paper provides a simple equational basis for the join, IRL∨LG, of the variety LG of lattice-ordered groups (ℓ-groups) and the variety IRL of integral residuated lattices.…

### Polynomial functions on subdirect products

- Mathematics
- 2010

A congruence preserving function on a subdirect product of two finite Mal’cev algebras is polynomial if it induces polynomial functions on the subdirect factors and there are no skew congruences…

### Near-rings of compatible functions

- MathematicsProceedings of the Edinburgh Mathematical Society
- 1980

Summary In this paper we study near-rings of functions on Ω-groups which are compatible with all congruence relations. Polynomial functions, for instance, are of this type. We employ the structure…

### Commutator theory for congruence modular varieties

- Mathematics
- 1989

Introduction In the theory of groups, the important concepts of Abelian group, solvable group, nilpotent group, the center of a group and centraliz-ers, are all defined from the binary operation [x,…