A juggler’s dozen of easy-/sup> problems

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• 作者：George F. McNulty
• 关键词：Primary ; 08Bxx ; Secondary ; 03C05 ; algebras ; lattices ; varieties ; finitely based ; dualizable
• 刊名：Algebra Universalis
• 出版年：2015
• 出版时间：September 2015
• 年：2015
• 卷：74
• 期：1-2
• 页码：17-34
• 全文大小：669 KB
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  8.Bentz, W., Davey, B.A., Pitkethly, J.G., Willard, R.: Dualizability of automatic algebras. J. Pure Appl. Algebra 218, 1324-345 (2014) http://?dx.?doi.?org/-0.-016/?j.?jpaa.-013.-1.-20
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  16.Clark, D.M., Davey, B.A., Pitkethly, J.G., Rifqui, D.L.: Flat unars: the primal, the semi-primal and the dualisable. Algebra Universalis 63, 303-29 (2010). http://?dx.?doi.?org/-0.-007/?s00012-010-0080-5 .
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  20.Davey, B.A., Idziak, P., Lampe, W.A., McNulty, G.F.: Dualizability and graph algebras. Discrete Math. 214, 145-72 (2000). http://?dx.?doi.?org/-0.-016/?S0012-365X(99)00225-3
  21.Davey, B.A., Jackson, M., Pitkethly, J.G., Talukder, M.R.: Natural dualities for semilattice-based algebras. Algebra Universalis 57, 463-90 (2007). http://?dx.?doi.?org/-0.-007/?s00012-007-2061-x
  22.Davey, B.A., Knox, B.J.: From rectangular bands to k-primal algebras. Semigroup Forum 64, 29-4 (2002). http://?dx.?doi.?org/-0.-007/?s002330010023
  23.DeMeo, W.: Interval enforceable properties of finite groups. Communications in Algebra (to appear)
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• 作者单位：George F. McNulty (1)
  
  1. Department of Mathematics, University of South Carolina, Columbia, SC, 29208, USA
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Algebra
  
• 出版者：Birkh盲user Basel
• ISSN：1420-8911

文摘

Is every dualizable finite algebra of finite signature finitely based? What is the likelihood that a random finite modular lattice directly decomposes into an even number of directly indecomposable lattices? Is the algebra \({\langle \mathbb{N},+, \cdot, {n\atopwithdelims ()k},!,0, 1 \rangle }\) finitely based? Is it decidable, given a finite lattice \({\mathbf{L}}\) and a finite algebra \({\mathbf{A}}\), whether \({\mathbf{L}}\) can be embedded into the congruence lattice of an algebra belonging to the variety generated by \({\mathbf{A}}\)? What is the Nullstellensatz for free lattices? Which finite automatic algebras are dualizable?