Work

A CHARACTERISATION OF SEMIGROUPS WITH ONLY COUNTABLY MANY SUBDIRECT PRODUCTS WITH $\mathbb {Z}$

Year: 2024

Type: article

Abstract: Let $\mathbb {Z}$ be the additive (semi)group of integers. We prove that for a finite semigroup S the direct product $\mathbb {Z}\times S$ contains only countably many subdirect products (up to isomorphism) if and only if S is regular. As a corollary we show that $\mathbb {Z}\times S$ has only countably many subsemigroups (up to isomorphism) if and only if S is completely regular.

Source: Bulletin of the Australian Mathematical Society

DOI: 10.1017/s0004972724000613

Authors: ASHLEY CLAYTON, CATHERINE REILLY, NIK RUŠKUC

Institutions: University of St Andrews, University of East Anglia

Language: English

Topic: semigroups and automata theory

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,450

OpenAlex ID: W4403143100