Definability for equational theories of commutative groupoids

Ježek, Jaroslav

doi:10.1007/s10587-012-0032-7

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2012

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“…In [9,10], Ježek obtained definability for some broad classes of varieties in GCOM and conjectured that the lattice GCOM has no nontrivial automorphisms.…”

Section: Introductionmentioning

confidence: 99%

On definability in some lattices of semigroup varieties

Grech

Sapir

2012

Semigroup Forum

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An identity of the form x 1 · · · x n ≈ x 1π x 2π · · · x nπ where π is a non-trivial permutation on the set {1, . . . , n} is called a permutation identity. If u ≈ v is a permutation identity, then (u ≈ v) [respectively r(u ≈ v)] is the maximal length of the common prefix For , r ≥ 0 and n > 1 let B ,r,n denote the set that consists of n! identities of the formwhere π is a permutation on the set {1, . . . , n}. We prove that for each permutative nilvariety V and each ≥ (V) and r ≥ r(V) there exists n > 1 such that V is definable by a first-order formula in L (var B l,r,n ) if = r or V is definable up to duality in L(var B ,r,n ) if = r.

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“…In [9,10], Ježek obtained definability for some broad classes of varieties in GCOM and conjectured that the lattice GCOM has no nontrivial automorphisms.…”

Section: Introductionmentioning

confidence: 99%

On definability in some lattices of semigroup varieties

Grech

Sapir

2012

Semigroup Forum

View full text Add to dashboard Cite

show abstract

Definability for equational theories of commutative groupoids

Cited by 1 publication

References 12 publications

On definability in some lattices of semigroup varieties

On definability in some lattices of semigroup varieties

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