A lattice is called close to distributive one if, instead of the strict distributivity identity, a “gap” of length at most 1 between the right and left parts of the identity is allowed. It was proven that the class of lattices that are minimal in class of lattices not close to distributive one can be divided into two subclasses. The first one consists of 3-generated lattices, the second one consists of 4-generated with respect to elements of a special type. The article gives a complete description of the subclass of 4-generated minimal lattices that are not close to distributive. This subclass contains 5 self-dual lattices and 12 pairs of dual lattices.
Keywords: lattice close to distributive one, modular lattice, lattice close to modular one, 4-generated lattice
Received January 29, 2026
Revised February 20, 2026
Accepted February 24, 2026
Funding Agency: The work was performed as part of research conducted in the Ural Mathematical Center with the financial support of the Ministry of Science and Higher Education of the Russian Federation (Agreement number 075-02-2026-737).
Kirill Vladimirovich Selivanov Ural Federal University, Yekaterinburg, 620000 Russia; Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences, Yekaterinburg, 620077 Russia, e-mail: ckirill2000@mail.ru
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Cite this article as: V.M. Sadovskii. Analysis of the mathematical model of a moment continuum that takes into account the irreversible deformation of a structurally inhomogeneous material. Trudy Instituta Matematiki i Mekhaniki URO RAN, 2026, vol. 32, no. 1, pp. 236–262.
