2018/12/31 by Ziba Fazelpour, Alireza Nasr-Isfahani · 3 citations
Mathematics · #Advanced Combinatorial Mathematics #Algebra over a field #Algebraic structures and combinatorial models #Characterization (materials science) #Commutative Algebra and Its Applications #Coxeter group #Ring (chemistry) #Type (biology) #math.RA #math.RT #msc:16D70 #msc:16G10 #msc:16G60
paper · pdf · doi:10.4153/s0008414x20000115
published in Canadian Journal of Mathematics 73(3), 656-686 (Cambridge University Press) · to appear in Canad. J. Math
openalex created_date 2018/12/22 · openalex publication_date 2020/02/24 · arxiv created 2020/09/30 · arxiv updated 2020/10/01 · openalex updated_date 2026/08/05
Abstract A ring \unicode[STIX]x1D6EC is called right Köthe if every right \unicode[STIX]x1D6EC -module is a direct sum of cyclic modules. In this paper, we give a characterization of basic hereditary right Köthe rings in terms of their Coxeter valued quivers. We also give a characterization of basic right Köthe rings with radical square zero. Therefore, we give a solution to Köthe’s problem in these two cases.