Trace ideals and uniserial modules
arXiv:2605.12459
The paper studies trace ideals of projective modules over the endomorphism ring of a uniserial module, characterizing when right‑hand trace ideals differ from left‑hand ones and providing an alternative construction of a non‑serial direct summand of a serial module.
Abstract
We thoroughly investigate the trace ideals of projective modules over the endomorphism ring of a uniserial module. After the work of Dubrovin and Puninski, it is known that this class of rings provides examples of trace ideals of projective right modules that are not trace ideals of projective left modules. In this paper we further investigate when this happens, giving an intrinsic description of such trace ideals and their properties. We also use the theory associated to lifting projective modules modulo a trace ideal to give an alternative approach to Puninski's construction of a direct summand of a serial module that is not serial.
27 pages. Comments and suggestions are welcome!