2022/04/15 by S. Dǎscǎlescu, Dascalescu, Sorin, C. Năstăsescu +3
Mathematics · #16D50 #16E50 #16G10 #16L60 #16S50 #16W50 #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2204.07639
openalex publication_date 2022/04/15 · openalex created_date 2022/04/28 · openalex updated_date 2026/07/28
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.