Profinite Congruences and Unary Algebras

J 2024

Profinite Congruences and Unary Algebras

ALMEIDA, Jorge a Ondřej KLÍMA

Základní údaje

Originální název

Profinite Congruences and Unary Algebras

Autoři

ALMEIDA, Jorge a Ondřej KLÍMA

Vydání

Journal of Multiple-Valued Logic and Soft Computing, Old City Publishing Inc, 2024, 1542-3980

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Spojené státy

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL, URL

Impakt faktor

Impact factor: 0.700

Označené pro přenos do RIV

Ano

Kód RIV

RIV/00216224:14310/24:00139497

Organizační jednotka

Přírodovědecká fakulta

UT WoS

001269856600002

EID Scopus

2-s2.0-85200538964

Klíčová slova anglicky

Profinite semigroup; profinite unary algebra; profinite congruence; Polish representation

Štítky

14311010, rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 31. 3. 2025 09:12, Mgr. Marie Novosadová Šípková, DiS.

Anotace

V originále

Profinite congruences on profinite algebras determining profinite quotients are difficult to describe. In particular, no constructive description is known of the least profinite congruence containing a given binary relation on the algebra. On the other hand, closed congruences and fully invariant congruences can be described constructively. In a previous paper, we conjectured that fully invariant closed congruences on a relatively free profinite algebra are always profinite. Here, we show that our conjecture fails for unary algebras and that closed congruences on relatively free profinite semigroups are not necessarily profinite. As part of our study of unary algebras, we establish an adjunction between profinite unary algebras and profinite monoids. We also show that the Polish representation of the free profinite unary algebra is faithful.

Návaznosti

GA19-12790S, projekt VaV

Název: Efektivní charakterizace tříd konečných pologrup a formálních jazyků

Investor: Grantová agentura ČR, Efektivní charakterizace tříd konečných pologrup a formálních jazyků

Citovat

ALMEIDA, Jorge a Ondřej KLÍMA. Profinite Congruences and Unary Algebras. Journal of Multiple-Valued Logic and Soft Computing. Old City Publishing Inc, 2024, roč. 42, č. 4, s. 265-297. ISSN 1542-3980.

@article{2421889,
   author = {Almeida, Jorge and Klíma, Ondřej},
   article_number = {4},
   keywords = {Profinite semigroup; profinite unary algebra; profinite congruence; Polish representation},
   language = {eng},
   issn = {1542-3980},
   journal = {Journal of Multiple-Valued Logic and Soft Computing},
   title = {Profinite Congruences and Unary Algebras},
   url = {https://www.oldcitypublishing.com/journals/mvlsc-home/mvlsc-issue-contents/mvlsc-volume-42-number-4-2024/mvlsc-42-4-p-265-297/},
   volume = {42},
   year = {2024}
}

TY  - JOUR
ID  - 2421889
AU  - Almeida, Jorge - Klíma, Ondřej
PY  - 2024
TI  - Profinite Congruences and Unary Algebras
JF  - Journal of Multiple-Valued Logic and Soft Computing
VL  - 42
IS  - 4
SP  - 265-297
EP  - 265-297
PB  - Old City Publishing Inc
SN  - 15423980
KW  - Profinite semigroup
KW  - profinite unary algebra
KW  - profinite congruence
KW  - Polish representation
UR  - https://www.oldcitypublishing.com/journals/mvlsc-home/mvlsc-issue-contents/mvlsc-volume-42-number-4-2024/mvlsc-42-4-p-265-297/
N2  - Profinite congruences on profinite algebras determining profinite quotients are difficult to describe. In particular, no constructive description is known of the least profinite congruence containing a given binary relation on the algebra. On the other hand, closed congruences and fully invariant congruences can be described constructively. In a previous paper, we conjectured that fully invariant closed congruences on a relatively free profinite algebra are always profinite. Here, we show that our conjecture fails for unary algebras and that closed congruences on relatively free profinite semigroups are not necessarily profinite. As part of our study of unary algebras, we establish an adjunction between profinite unary algebras and profinite monoids. We also show that the Polish representation of the free profinite unary algebra is faithful.
ER  -

ALMEIDA, Jorge a Ondřej KLÍMA. Profinite Congruences and Unary Algebras. \textit{Journal of Multiple-Valued Logic and Soft Computing}. Old City Publishing Inc, 2024, roč.~42, č.~4, s.~265-297. ISSN~1542-3980.

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