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@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://ui.adsabs.harvard.edu/abs/2020arXiv200300509A/abstract},
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://ui.adsabs.harvard.edu/abs/2020arXiv200300509A/abstract
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 and Ondřej KLÍMA. Profinite Congruences and Unary Algebras. \textit{Journal of Multiple-Valued Logic and Soft Computing}. Old City Publishing Inc, 2024, vol.~42, No~4, p.~265-297. ISSN~1542-3980.
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