Preserving near unanimity terms under products

Campanella, Maria; Conley, Sean; Valeriote, Matthew

doi:10.1007/s00012-016-0393-0

Cited by 6 publications

(5 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Our constructions might share some aspects in common with the above-mentioned works; we have not fully checked this. Other papers which might contain constructions bearing some resemblance with the present ones are [3,8].…”

Section: Some More Explicit Descriptions and Summing Up Everythingmentioning

confidence: 92%

Day's Theorem is sharp for $n$ even

Lipparini¹

2019

Preprint

View full text Add to dashboard Cite

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 Jónsson terms t 0 , . . . , tn witnessing congruence distributivity it is possible to construct terms u 0 , . . . , u 2n−1 witnessing congruence modularity. We show that Day's result about the number of such terms is sharp when n is even. We also deal with other kinds of terms, such as alvin, Gumm, directed, specular, mixed and defective.All the results hold also when restricted to locally finite varieties. We introduce some families of congruence distributive varieties and characterize many congruence identities they satisfy.

show abstract

Section: Some More Explicit Descriptions and Summing Up Everythingmentioning

confidence: 92%

Day's Theorem is sharp for $n$ even

Lipparini¹

2019

Preprint

View full text Add to dashboard Cite

show abstract

“…Example 4.4 was discovered with the help of UACalc, a universal algebra calculator. After including it here we learned that the preprint [6] by Campenella, Conley and Valeriote contains essentially the same example. We are informed that they also discovered the example with the help of UACalc.…”

Section: The Influence Of Finite Signaturementioning

confidence: 98%

Cube term blockers without finiteness

Kearnes

Szendrei

2017

Algebra Univers.

View full text Add to dashboard Cite

Abstract. We show that an idempotent variety has a d-dimensional cube term if and only if its free algebra on two generators has no d-ary compatible cross. We employ Hall's Marriage Theorem to show that a variety of finite signature whose fundamental operations have arities n 1 , . . . , n k has a d-dimensional cube term if and only if it has one of dimension d = 1 + k i=1 (n i − 1). This lower bound on dimension is shown to be sharp. We show that a pure cyclic term variety has a cube term if and only if it contains no 2-element semilattice. We prove that the Maltsev condition "existence of a cube term" is join prime in the lattice of idempotent Maltsev conditions.

show abstract

“…In [9] Campanella, Conley, Valeriote proved that if V and W are idempotent varieties of the same type and with, respectively, an n-near-unanimity term and an m-near-unanimity term, then both the join and the Maltsev product [12] of V and W have an n+m−1-near-unanimity term. Moreover, they show by a counterexample that the result is the best possible.…”

Section: Some Problemsmentioning

confidence: 99%

“…Problem 7.8. Do the results from [9] hold also when one or both n and m are half-integers? Possibly, one needs to modify the definition of a n 1 2 -near-unanimity term as in Remark 6.2 and Corollary 6.3.…”

Section: Some Problemsmentioning

confidence: 99%