On a locality-like property of the pseudovariety J

J 2018

On a locality-like property of the pseudovariety J

KAĎOUREK, Jiří

Základní údaje

Originální název

On a locality-like property of the pseudovariety J

Autoři

KAĎOUREK, Jiří

Vydání

Periodica mathematica Hungarica, Budapest, Akadémiai Kiadó, 2018, 0031-5303

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Maďarsko

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 0.664

Označené pro přenos do RIV

Ano

Kód RIV

RIV/00216224:14310/18:00106425

Organizační jednotka

Přírodovědecká fakulta

Klíčová slova anglicky

Pseudovarieties of finite monoids and finite categories; Locally finite varieties of monoids and categories; Finitely generated relatively free monoids and categories; Semidirect products of pseudovarieties of finite monoids

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 1. 3. 2019 16:58, doc. RNDr. Jiří Kaďourek, CSc.

Anotace

V originále

It is well known that the pseudovariety J of all J-trivial monoids is not local, which means that the pseudovariety gJ of categories generated by J is a proper subpseudovariety of the pseudovariety lJ of categories all of whose local monoids belong to J. In this paper, it is proved that the pseudovariety J enjoys the following weaker property. For every prime number p, the pseudovariety lJ is a subpseudovariety of the pseudovariety g(J*Abp), where Abp is the pseudovariety of all elementary abelian p-groups and J*Abp is the pseudovariety of monoids generated by the class of all semidirect products of monoids from J by groups from Abp. As an application, a new proof of the celebrated equality of pseudovarieties PG=BG is obtained, where PG is the pseudovariety of monoids generated by the class of all power monoids of groups and BG is the pseudovariety of all block groups.

Citovat

KAĎOUREK, Jiří. On a locality-like property of the pseudovariety J. Periodica mathematica Hungarica. Budapest: Akadémiai Kiadó, 2018, roč. 76, č. 1, s. 1-46. ISSN 0031-5303. Dostupné z: https://doi.org/10.1007/s10998-017-0186-z.

@article{1502220,
   author = {Kaďourek, Jiří},
   article_location = {Budapest},
   article_number = {1},
   doi = {https://doi.org/10.1007/s10998-017-0186-z},
   keywords = {Pseudovarieties of finite monoids and finite categories; Locally finite varieties of monoids and categories; Finitely generated relatively free monoids and categories; Semidirect products of pseudovarieties of finite monoids},
   language = {eng},
   issn = {0031-5303},
   journal = {Periodica mathematica Hungarica},
   title = {On a locality-like property of the pseudovariety J},
   url = {https://link.springer.com/content/pdf/10.1007%2Fs10998-017-0186-z.pdf},
   volume = {76},
   year = {2018}
}

TY  - JOUR
ID  - 1502220
AU  - Kaďourek, Jiří
PY  - 2018
TI  - On a locality-like property of the pseudovariety J
JF  - Periodica mathematica Hungarica
VL  - 76
IS  - 1
SP  - 1-46
EP  - 1-46
PB  - Akadémiai Kiadó
SN  - 00315303
KW  - Pseudovarieties of finite monoids and finite categories
KW  - Locally finite varieties of monoids and categories
KW  - Finitely generated relatively free monoids and categories
KW  - Semidirect products of pseudovarieties of finite monoids
UR  - https://link.springer.com/content/pdf/10.1007%2Fs10998-017-0186-z.pdf
L2  - https://link.springer.com/content/pdf/10.1007%2Fs10998-017-0186-z.pdf
N2  - It is well known that the pseudovariety J of all J-trivial monoids is not local, which means that the pseudovariety gJ of categories generated by J is a proper subpseudovariety of the pseudovariety lJ of categories all of whose local monoids belong to J. In this paper, it is proved that the pseudovariety J enjoys the following weaker property. For every prime number p, the pseudovariety lJ is a subpseudovariety of the pseudovariety g(J*Abp), where Abp is the pseudovariety of all elementary abelian p-groups and J*Abp is the pseudovariety of monoids generated by the class of all semidirect products of monoids from J by groups from Abp. As an application, a new proof of the celebrated equality of pseudovarieties PG=BG is obtained, where PG is the pseudovariety of monoids generated by the class of all power monoids of groups and BG is the pseudovariety of all block groups.
ER  -

KAĎOUREK, Jiří. On a locality-like property of the pseudovariety J. \textit{Periodica mathematica Hungarica}. Budapest: Akadémiai Kiadó, 2018, roč.~76, č.~1, s.~1-46. ISSN~0031-5303. Dostupné z: https://doi.org/10.1007/s10998-017-0186-z.

Přehled o publikaci