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On quasi-identities of finite modular lattices. II [PDF]
Қарағанды университетінің хабаршысы. Математика сериясы, 2023 The existence of a finite identity basis for any finite lattice was established by R. McKenzie in 1970, but the analogous statement for quasi-identities is incorrect.
A.O. Basheyeva, S.M. Lutsak
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Direct summands of Goldie extending elements in modular lattices [PDF]
Mathematica Bohemica, 2022 In this paper some results on direct summands of Goldie extending elements are studied in a modular lattice. An element $a$ of a lattice $L$ with $0$ is said to be a Goldie extending element if and only if for every $b \leq a$ there exists a direct ...
Rupal Shroff
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On quasi-identities of finite modular lattices
Вестник КазНУ. Серия математика, механика, информатика, 2022 In 1970 R. McKenzie proved that any finite lattice has a finite basis of identities. However the similar result for quasi-identities is not true. That is there is a finite lattice that has no finite basis of quasi-identities.
S. Lutsak, O. Voronina, G. Nurakhmetova
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SOME PROPERTIES ON DERIVATIONS OF LATTICES [PDF]
Journal of Algebraic Systems, 2021 In this paper we consider some properties of derivations of lattices and show that (i) for a derivation $d$ of a lattice $L$ with the maximum element $1$, it is monotone if and only if $d(x) \le d(1)$ for all $x\in L$ (ii) a monotone derivation $d$ is ...
Mayuka Kawaguchi, Michiro KONDO
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On some new developments in the theory of subgroup lattices of groups [PDF]
International Journal of Group Theory, 2023 A rather natural way for trying to obtain a lattice-theoretic characterization of a class of groups ${\mathcal X}$ is to replace the concepts appearing in the definition of ${\mathcal X}$ by lattice-theoretic concepts.
Maria De Falco, Carmela Musella
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Cryptography, 2023 The Number Theoretic Transform (NTT) has been widely used to speed up polynomial multiplication in lattice-based post-quantum algorithms. All NTT operands use modular arithmetic, especially modular multiplication, which significantly influences NTT ...
Trong-Hung Nguyen +2 more
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Pasting and modular lattices [PDF]
Proceedings of the American Mathematical Society, 1989 A classical lattice construction of R. P. Dilworth is the gluing of two lattices. A number of recent papers by A. Slavík, A. Day, and J. Ježek investigated a generalization: pasting .
Fried, E., Grätzer, G.
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Some non-standard quasivarieties of lattices [PDF]
Қарағанды университетінің хабаршысы. Математика сериясы, 2023 The questions of the standardness of quasivarieties have been investigated by many authors. The problem "Which finite lattices generate a standard topological prevariety?" was suggested by D.M. Clark, B.A. Davey, M.G. Jackson and J.G. Pitkethly in 2008.
S.M. Lutsak +3 more
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Equivalent Forms for a Poset to Be Modular Poset
Discussiones Mathematicae - General Algebra and Applications, 2021 The notion of modular and distributive posets which generalize the corresponding notions from the lattice theory are introduced by J. Larmerova and J. Rachnek.
Sundarayya P., Kishore T. Ravi
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THE LATTICE OF CONGRUENCES ON A TERNARY SEMIGROUP [PDF]
Journal of Algebraic Systems, 2018 In this paper we investigate some properties of congruences on ternary semigroups. We also define the notion of congruence on a ternary semigroup generated by a relation and we determine the method of obtaining a congruence on a ternary semigroup T from a
N. Ashrafi, Z. Yazdanmehr
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