2024/04/26 by Peter Mayr, Nik Ruškuc, Mayr, Peter +1 · 1 citation
Computer Science · Mathematics · #03C05 (20B27 #06E15 #08A05 #22A05 #54H10) #Advanced Algebra and Logic #Commutative Algebra and Its Applications #FOS: Mathematics #Group Theory (math.GR) #Logic (math.LO) #Rings and Algebras (math.RA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2404.17322
openalex publication_date 2024/04/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let A be a finite simple non-abelian Mal'cev algebra (e.g. a group, loop, ring). We investigate the Boolean power D of A by the countable atomless Boolean algebra B filtered at some idempotents e1,…,en of A. When e1,…,en are all idempotents of A we establish two concrete representations of D: as the Fraïssé limit of the class of finite direct powers of A, and as congruence classes of the countable free algebra in the variety generated by A. Further, for arbitrary e1,…,en, we show that D is ω-categorical and that its automorphism group has the small index property, strong uncountable cofinality and the Bergman property. As necessary background we establish some general properties of congruences and automorphisms of filtered Boolean powers of A by any Boolean algebra B, including a semidirect decomposition for their automorphism groups.