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Izv. Vyssh. Uchebn. Zaved. Mat., 2016, Number 3, Pages 18–22 (Mi ivm9088)  

Finitely generated lattices with $M$-standard elements among generators

A. G. Gein

Chair of Algebra and Discrete Mathematics, Ural Federal University, 19 Mira str., Ekaterinburg, 620002 Russia

Abstract: We prove that a lattice is modular if it is generated by three elements, two of which are $M$-standard. We also show that a lattice generated by $n$, $n>3$, $M$-standard elements must not necessarily be modular.

Keywords: modular lattice, left-modular element, right-modular element, $M$-standard element.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 02.A03.21.0006


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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2016, 60:3, 14–17

Bibliographic databases:

UDC: 512.565
Received: 13.08.2014

Citation: A. G. Gein, “Finitely generated lattices with $M$-standard elements among generators”, Izv. Vyssh. Uchebn. Zaved. Mat., 2016, no. 3, 18–22; Russian Math. (Iz. VUZ), 60:3 (2016), 14–17

Citation in format AMSBIB
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  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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