University of KashanMathematics Interdisciplinary Research2538-36397420221201S-Acts with Finitely Generated Universal Congruence37738411290510.22052/mir.2022.246505.1357ENAli AsgharGholipourDepartment of Mathematics,
Science and Research Branch,
Islamic Azad University,
Tehran, Iran0000-0002-8473-2246HasanBarzegarDepartment of Mathematics,
Tafresh University, 39518-79611, Tafresh, Iran0000-0002-8916-7733HamidRasoliDepartment of Mathematics,
Science and Research Branch,
Islamic Azad University,
Tehran, IranAbolfazlTehranianDepartment of Mathematics,
Science and Research Branch,
Islamic Azad University,
Tehran, IranJournal Article20220619Universal left congruences on semigroups were studied in “Y. Dandan, V. Gould, T. Quinn-Gregson and R. Zenab, Semigroups with finitely generated universal left congruence, Monat. Math. 190 (2019) 689−724”. We consider universal congruences on acts over monoids and extend the results from semigroups to acts. Among other things, for an S-act A<sub>S</sub> with zero over a monoid S, we prove that being finitely generated of the universal congruence ω<sub>A</sub> and being pseudofinite of A<sub>S</sub> coincide.https://mir.kashanu.ac.ir/article_112905_d254330567fbf36eaca6f1309f1c9f77.pdf