A short way to directed Jónsson terms
Choose format
RIS BIB ENDNOTEA short way to directed Jónsson terms
Publication date: 12.12.2024
Reports on Mathematical Logic, 2024, Number 59, pp. 79-95
https://doi.org/10.4467/20842589RM.24.001.20699Authors
A short way to directed Jónsson terms
We show that a variety with J´onsson terms t1, . . . , tn–1 has directed J´onsson terms d1, . . . , dn–1 for the same value of the indices, solving a problem raised by Kazda et al. Refined results are obtained for locally finite varieties.
[1] L. Barto, Finitely related algebras in congruence modular varieties have few subpowers, J. Eur. Math. Soc. (JEMS) 20, 1439-1471 (2018)
[2] L. Barto, M. Kozik, Absorption in universal algebra and CSP, in: The Constraint Satisfaction Problem: Complexity and Approximability , Dagstuhl Follow-Ups, 7 (Schloss Dagstuhl-Leibniz Zentrum fur Informatik, Wadern, 2017), 45-77
[3] T. Dent, K. A. Kearnes and A. Szendrei, An easy test for congruence modularity, Algebra Universalis 67, 375-392 (2012).
[4] R. Freese, M. A. Valeriote, On the complexity of some Maltsev conditions, Internat. J. Algebra Comput. 19, 41-77 (2009).
[5] G. Gyenizse, M. Maroti, Quasiorder lattices of varieties, Algebra Universalis, 79, Paper No. 38, 17 (2018).
[6] B. Jonsson, Algebras whose congruence lattices are distributive, Math. Scand. 21, 110-121 (1967).
[7] A. Kazda, M. Kozik, R. McKenzie, M. Moore, Absorption and directed Jonsson terms, in: J. Czelakowski (ed.), Don Pigozzi on Abstract Algebraic Logic, Universal Algebra, and Computer Science, Outstanding Contributions to Logic 16, Springer, Cham, 203-220 (2018).
[8] A. Kazda, M. Valeriote, Deciding some Maltsev conditions in finite idempotent algebras, J. Symb. Logic 85, 539-562 (2020).
[9] M. Kozik, Directed SD(_) terms, preprint.
[10] P. Lipparini, The Jonsson distributivity spectrum, Algebra Universalis 79 no. 2, Art. 23, 16 (2018).
[11] P. Lipparini, Unions of admissible relations and congruence distributivity, Acta Math. Univ. Comenian. 87 (2), 251-266 (2018).
[12] P. Lipparini, Day's Theorem is sharp for n even. arXiv:1902.05995v7, 1-64 (2021).
[13] R. McKenzie, Monotone clones, residual smallness and congruence distributivity, Bull. Austral. Math. Soc. 41, 283-300 (1990).
[14] R. N. McKenzie, G. F. McNulty, W. F. Taylor, Algebras, Lattices, Varieties. Vol. I, Wadsworth & Brooks/Cole Advanced Books & Software (1987), corrected reprint with additional bibliography, AMS Chelsea Publishing/American Mathematical Society (2018).
[15] L. Zadori, Monotone Jonsson operations and near unanimity functions, Algebra Universalis 33, 216-236 (1995).
Information: Reports on Mathematical Logic, 2024, Number 59, pp. 79-95
Article type: Original article
The University of Rome Tor Vergata, Roma
Italy
Published at: 12.12.2024
Received at: 11.05.2024
Article status: Open
Licence: CC BY
Article financing:
Percentage share of authors:
Classification number:
Article corrections:
-Publication languages:
English