Universal monoid actions: The power of freedom

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F25%3A00637744" target="_blank" >RIV/67985840:_____/25:00637744 - isvavai.cz</a>

Result on the web

<a href="https://doi.org/10.1090/proc/17309" target="_blank" >https://doi.org/10.1090/proc/17309</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1090/proc/17309" target="_blank" >10.1090/proc/17309</a>

Result language

angličtina

Original language name

Universal monoid actions: The power of freedom

Original language description

Motivated by the recent work of Balcerzak and Kania [Proc. Amer. Math. Soc. 151 (2023) pp. 3737–3742], we show that every countable monoid has a universal action on the free object over a countable infinite set. This is a general result concerning concrete categories with a left adjoint (free) functor. On the way, we introduce an abstract concept of 'being generated by a set'. At the same time we obtain a simpler proof of the result of Darji and Matheron [Proc. Amer. Math. Soc. 145 (2017), pp. 251–265] concerning a surjectively universal operator on the classical Banach space ℓ1 of summable sequences.

Czech name

—

Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10101 - Pure mathematics

Project

—

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2025

Confidentiality

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

Name of the periodical

Proceedings of the American Mathematical Society

ISSN

0002-9939

e-ISSN

1088-6826

Volume of the periodical

153

Issue of the periodical within the volume

9

Country of publishing house

US - UNITED STATES

Number of pages

11

Pages from-to

3635-3645

UT code for WoS article

001522392700001

EID of the result in the Scopus database

2-s2.0-105011405786