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Bibliography
Balbes, R.: A note on distributive sublattices of a modular lattice. Fundam. Math. 65(2), 219–222 (1969)
Bergman, C.: Universal Algebra: Fundamentals and Selected Topics. CRC, Boca Raton/London/New York (2011)
Day, A., Freese, R.: A characterization of identities implying congruence modularity. Can. J. Math. 32, 1140–1167 (1980)
Erné, M.: Weak distributive laws and their role in lattices of congruences and equational theories. Algebra Univers. 25, 290–321 (1988)
Freese, R., McKenzie, R.N.: Commutator Theory for Congruence Modular Varieties. London Mathematical Society Lecture Note Series, vol. 125. Cambridge University Press, Cambridge/New York (1987). The second edition is available online
Grätzer, G.: General Lattice Theory. Akademie, Berlin (1978)
Gumm, H.P.: Geometrical Methods in Congruence Modular Algebras. Mem. Am. Math. Soc. 45, 286 (1983)
Hobby, D., McKenzie, R.N.: The Structure of Finite Algebras. Contemporary Mathematics, vol. 76. American Mathematical Society, Providence (1988)
Idziak, P.: Elementary theory of finite equivalential algebras. Rep. Math. Log. 25, 81–89 (1991)
Idziak, P.M., Słomczyńska, K., Wroński, A.: Commutator in equivalential algebra and Fregean varieties. Algebra Univers. 65, 331–340 (2011)
Jónsson, B.: Distributive sublattices of a modular lattice. Proc. Am. Math. Soc. 6, 682–688 (1955)
Kearnes, K.A.: Varieties with a difference term. J. Algebra 177, 926–960 (1995)
Kearnes, K.A.: Almost all minimal idempotent varieties are congruence modular. Algebra Univers. 44, 39–45 (2000)
Kearnes, K.A.: Congruence join-semidistributivity is equivalent to a congruence identity. Algebra Univers. 46, 373–387 (2001)
Kearnes, K.A., Kiss, E.W.: The shape of congruence lattices. Mem. Am. Math. Soc. 222, 1046 (2013)
Kearnes, K.A., McKenzie, R.N.: Commutator theory for relatively modular quasivarieties. Trans. Am. Math. Soc. 331(2), 465–502 (1992)
Kearnes, K.A., Szendrei, Á.: The relationship between two commutators. Int. J. Algebra Comput. 8, 497–531 (1998)
Kiss, E.W.: Three remarks on the modular commutator. Algebra Univers. 29, 455–476 (1992)
McKenzie, R.N.: Finite equational bases for congruence modular varieties. Algebra Univers. 24, 224–250 (1987)
Słomczyńska, K.: Equivalential algebras. Part I: Representation Algebra Univers. 35, 524–547 (1996)
Tamura, S.: A note on distributive sublattices of a lattice. Proc. Jpn. Acad. 47, 603–605 (1971)
von Neumann, J.: Lectures on Continuous Geometries. Institute of Advanced Studies, Princeton (1936–1937)
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Czelakowski, J. (2015). Modularity and Related Topics. In: The Equationally-Defined Commutator. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-21200-5_6
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