2020/08/25 by Be’eri Greenfeld, Greenfeld, Be'eri, Louis Rowen +1
Mathematics · #16R20 #16U20 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Primary 16P40 #Representation Theory (math.RT) #Rings and Algebras (math.RA) #Secondary 16S10
paper · pdf · doi:10.48550/arxiv.2008.11041
openalex publication_date 2020/08/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This note concerns the still open question of representability of Noetherian PI-algebras. Extending a result of Rowen and Small (with an observation of Bergman) that every finitely generated module over a commutative Noetherian ring containing a field is representable, we provide a representability machinery for a Noetherian PI-algebra R containing a field, which includes the case that R is finite (as a module) over a commutative subalgebra isomorphic to R/N. We construct a family of non-representable PI-algebras demonstrating the sharpness of these results, as well as of some well known previous representability results.