Links, localizations and factorizations

Time: 9:30 -- 11: 00, April 23, 2025

Venue: Room 612, A6, Institute of Mathematics-VAST

Abstract: Farber and Vogel used link modules, i.e., Sato modules to characterize a specific universal Cohn localization of a group algebra of a free associative group. In this work we discuss interrelations between Cohn localizations of square matrices, a Leavitt localization of a row and the Jacobson quasi-inverses of quasi-regular elements. The latter Jacobson localizations appear naturally and easily in rings which are complete with respect to an ideal topology, pointing out also a connection to specific Gabriel localizations. As a main result and an application we develop a factorization theory for polynomials in group algebras of free associative groups with non-zero augmentation.