2025/11/07 by Banerjee, Sourayan, Kuber, Amit
Mathematics · #03C60 #19B14 #19B99 #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Logic (math.LO) #Rings, Modules, and Algebras
paper · doi:10.48550/arxiv.2511.05180
openalex publication_date 2025/11/07 · openalex created_date 2025/11/11 · openalex updated_date 2026/07/28
This paper is a sequel to a paper by the same authors, where they defined K-groups of model-theoretic structures, and computed K1 of free modules over PIDs. In this paper, we compute K1 of a right Mq(R)-module M, where R is a division ring, q≥1, and |Mq(R)|≠ 2. As a consequence, we obtain a (weak) Morita invariance K1(RR)≅ K1((Mq(R))Mq(R)) for all division rings R and q≥ 1. Finally, we compute K1 of a module over a semisimple ring by showing that the model-theoretic K1 commutes with finite product of modules. We also show that the algebraic K1 of a finite product of infinite matrix rings embeds into the model-theoretic K1 of their right regular modules.