Nespočetně mnoho variet úplně jednoduchých pologrup s metabelovskými podgrupami

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F06%3A00017888" target="_blank" >RIV/00216224:14310/06:00017888 - isvavai.cz</a>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Uncountably many varieties of completely simple semigroups with metabelian subgroups

Popis výsledku v původním jazyce

It has been proved by D. E. Cohen in 1967 that the lattice of all varieties of metabelian groups is countable. In this paper, we show that the lattice of all varieties of completely simple semigroups with metabelian subgroups has the cardinality of the continuum. M. Petrich and N. R. Reilly have introduced in a paper of 1983 the notion of near varieties of idempotent generated completely simple semigroups. The mapping assigning to every variety V of completely simple semigroups the class of all idempotent generated members of V is a complete lattice homomorphism of the lattice of all varieties of completely simple semigroups onto the lattice of all near varieties of idempotent generated completely simple semigroups. In this paper we show that, in fact,the lattice of all near varieties of idempotent generated completely simple semigroups with metabelian subgroups has itself the cardinality of the continuum.

Název v anglickém jazyce

Uncountably many varieties of completely simple semigroups with metabelian subgroups

Popis výsledku anglicky

It has been proved by D. E. Cohen in 1967 that the lattice of all varieties of metabelian groups is countable. In this paper, we show that the lattice of all varieties of completely simple semigroups with metabelian subgroups has the cardinality of the continuum. M. Petrich and N. R. Reilly have introduced in a paper of 1983 the notion of near varieties of idempotent generated completely simple semigroups. The mapping assigning to every variety V of completely simple semigroups the class of all idempotent generated members of V is a complete lattice homomorphism of the lattice of all varieties of completely simple semigroups onto the lattice of all near varieties of idempotent generated completely simple semigroups. In this paper we show that, in fact,the lattice of all near varieties of idempotent generated completely simple semigroups with metabelian subgroups has itself the cardinality of the continuum.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

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Návaznosti

Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2006

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Glasgow Mathematical Journal

ISSN

0017-0895

e-ISSN

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Svazek periodika

48

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

46

Strana od-do

365-410

Kód UT WoS článku

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EID výsledku v databázi Scopus

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