The largest higher commutator sequence

• Autorzy: Mudrinski Nebojša

Identyfikatory

DOI

10.4467/20842589RM.19.004.10652

• Języki publikacji: EN

Abstrakty

EN

Given the congruence lattice L of a finite algebra A that generates a congruence permutable variety, we look for those sequences of operations on L that have the properties of higher commutator operations of expansions of A. If we introduce the order of such sequences in the natural way the question is whether exists or not the largest one. The answer is positive. We provide a description of the largest element and as a consequence we obtain that the sequences form a complete lattice.

Słowa kluczowe

EN

lattices; sequences of operations; commutators

• Wydawca: Wydawnictwo Uniwersytetu Jagiellońskiego
• Czasopismo: Reports on Mathematical Logic
• Rocznik: 2019
• Tom: Vol. 54
• Strony: 83--94
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Mudrinski Nebojša

• Department of Mathematics and Informatics Faculty of Sciences University of Novi Sad 21000 Novi Sad, Serbia

Bibliografia

• [1] E. Aichinger and N. Mudrinski, Some applications of higher commutators in Mal’cev algebras, Algebra Universalis 63:4 (2010), 367–403.
• [2] E. Aichinger and N. Mudrinski, Sequences of commutator operations, Order 30 (2013), 859–867.
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• [6] J. Czelakowski, Additivity of the commutator and residuation, Rep. Math. Logic 43 (2008), 109–132.
• [7] J. Czelakowski, The Equationally-Defined Commutator: A study in equational logic and algebra, Birkh¨auser/Springer, Cham, 2015.
• [8] J. Czelakowski, The equationally defined commutator in quasivarieties generated by two-element algebras, Outstanding Contributions to Logic 16, Don Pigozzi on Abstract Algebraic Logic, Universal Algebra and Computer Science, Springer, Cham, 2018, pp. 131–165.
• [9] R. Freese and R.N. McKenzie, Commutator theory for congruence modular varieties, London Math. Soc. Lecture Note Ser., Vol. 125, Cambridge University Press, 1987.
• [10] R.N. McKenzie, G.F. McNulty, and W.F. Taylor, Algebras, lattices, varieties, Vol. 1, Wadsworth & Brooks / Cole Advanced Books & Software, Monterey, California, 1987.
• [11] A. Moorhead, Higher commutator theory for congruence modular varieties, Journal of Algebra 513 (2018), 133–158.
• [12] N. Mudrinski, On Polynomials in Mal’cev Algebras, Ph.D. thesis, University of Novi Sad, 2009. Available at:http://people.dmi.uns.ac.rs/˜ nmudrinski/DissertationMudrinski.pdf.
• [13] J.D.H. Smith, Mal’cev varieties, Lecture Notes in Math., Vol. 554, Springer Verlag, Berlin, 1976.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).