Graded Frobenius Rings
Rings and Algebras
2022-04-19 v1
Abstract
In order to study graded Frobenius algebras from a ring theoretical perspective, we introduce graded quasi-Frobenius rings, graded Frobenius rings and a shift-version of the latter ones, and we investigate the structure and representations of such objects. We need to revisit graded simple graded left Artinian rings, graded semisimple rings, and to provide graded versions of certain results concerning the Jacobson radical, the singular radical, and their connection to finiteness conditions and injectivity. We prove a structure result for (shift-)graded Frobenius rings.
Cite
@article{arxiv.2204.07639,
title = {Graded Frobenius Rings},
author = {Sorin Dascalescu and Constantin Nastasescu and Laura Nastasescu},
journal= {arXiv preprint arXiv:2204.07639},
year = {2022}
}