On finiteness of 3-generated lattice with left modular and separating elements among generators
Mikhail P. Shushpanov · Russian Mathematics · 2019
Îäíèì èç ïðîäóêòèâíûõ ìåòîäîâ èññëåäîâàíèÿ ðåøåòîê ÿâèëîñü ðàññìîòðåíèå â íèõ ýëåìåíòîâ, îáëàäàþùèõ ñâîéñòâàìè, ëîêàëèçóþùèìè ïîíÿòèå ìîäóëÿðíîñòè.Òàêàÿ ëîêàëèçàöèÿ îñóùåñòâëÿåòñÿ ïî åäèíîé ñõåìå: â êâàçèòîæäåñòâå, âûðàæàþùåì çàêîí ìîäóëÿðíîñòè, êâàíòîð âñåîáùíîñòè ïðèìåíÿåòñÿ òîëüêî ê äâóì ýëåìåíòàì èç òðåõ, è îñòàâøèéñÿ ñâîáîäíûì òðåòèé ýëåìåíò, äëÿ êîòîðîãî îêàçûâàåòñÿ èñòèííûì ñêîíñòðóèðîâàííîå òàêèì îáðàçîì âûñêàçûâàíèå, è ïîëó÷àåò ñîîòâåòñòâóþùåå íàçâàíèå. ñèëó ýòîãî êàæäûé ðàçäåëÿþùèé ýëåìåíò ëåâîìîäóëÿðåí.Ïîñòóïèëà â ðåäàêöèþ 24.10.2018,ïîñëå äîðàáîòêè 24.10.2018.Ïðèíÿòà ê ïóáëèêàöèè 19.12.2018Áëàãîäàðíîñòè.Ðàáîòà âûïîëíåíà ïðè ôèíàíñîâîé ïîääåðæêå â ðàìêàõ ïðîåêòà ïîâûøåíèÿ êîíêóðåíòîñïîñîáíîñòè (Ñîãëàøåíèå ìåæäó Ìèíèñòåðñòâîì îáðàçîâàíèÿ è íàóêè Ðîññèéñêîé Ôåäåðàöèè è Óðàëüñêèì ôåäåðàëüíûì óíèâåðñèòåòîì îò 27.08.2013,02.A03.21.0006).On niteness of 3-generated lattice with left modular and separating elements among generators Abstract.We prove that a 3-generated lattice with modular and separating generators contains at most fourty seven elements.This estimate is stated to be sharp.