This article is cited in 1 paper

Mathematical logic, algebra and number theory

Pseudofinite $S$-acts

A. A. Stepanova, E. L. Efremov, S. G. Chekanov

Far Eastern Federal University, 10 Ajax Bay, Russky Island, 690922, Vladivostok, Russia

Abstract: The work has begun to study the structure of pseudofinite acts over a monoid. A theorem on the finiteness of an arbitrary cyclic subacts of $S$-act is proved under the condition that this $S$-act is pseudofinite and the number of types of isomorphisms of finite cyclic $S$-acts is finite. It is shown that a coproduct of finite $S$-acts is pseudofinite. As a consequence, it is shown that any $S$-act, where $S$ is a finite group, is pseudofinite.

Keywords: pseudofinite act, pseudofinite theory, coproduct, act over monoid.

UDC: 510.67, 512.57

MSC: 03C

Received November 10, 2023, published April 8, 2024

Language: English

DOI: 10.33048/semi.2024.21.020