2013/10/02 by Alex Bailey, Bailey, Alex, James Renshaw +1 · 1 citation
Computer Science · #20M50 #Computability, Logic, AI Algorithms #FOS: Mathematics #Group Theory (math.GR) #Logic, programming, and type systems #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1310.0742
openalex publication_date 2013/10/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Recently two different concepts of covers of acts over monoids have been studied. That based on coessential epimorphisms and that based on Enochs' definition of a flat cover of a module over a ring. Two recent papers have suggested that in the former case, strongly flat covers are not unique. We show that these examples are in fact false and so the question of uniqueness appears to still remain open. In the latter case, we re-present an example due to Kruml that demonstrates that, unlike the case for flat covers of modules, strongly flat covers of S-acts do not always exist.