Detailed Information on Publication Record
2024
Profinite Congruences and Unary Algebras
ALMEIDA, Jorge and Ondřej KLÍMABasic information
Original name
Profinite Congruences and Unary Algebras
Authors
ALMEIDA, Jorge and Ondřej KLÍMA (203 Czech Republic, belonging to the institution)
Edition
Journal of Multiple-Valued Logic and Soft Computing, Old City Publishing Inc, 2024, 1542-3980
Other information
Language
English
Type of outcome
Článek v odborném periodiku
Field of Study
10101 Pure mathematics
Country of publisher
United States of America
Confidentiality degree
není předmětem státního či obchodního tajemství
Impact factor
Impact factor: 1.300 in 2022
Organization unit
Faculty of Science
UT WoS
001269856600002
Keywords in English
Profinite semigroup; profinite unary algebra; profinite congruence; Polish representation
Tags
Tags
International impact, Reviewed
Změněno: 7/8/2024 11:22, Mgr. Marie Šípková, DiS.
Abstract
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.
Links
| GA19-12790S, research and development project |
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