2023/05/22 by Bennett-Tennenhaus, Raphael
#16H10 #16L30 #FOS: Mathematics #Primary 16G30 #Representation Theory (math.RT) #Rings and Algebras (math.RA) #Secondary 16G20
paper · doi:10.48550/arxiv.2305.12885
For a path algebra over a noetherian local ground ring, the notion of an admissible ideal was defined by Raggi-Cárdenas and Salmerón. We provide sufficient conditions for admissibility and use them to study semiperfect module-finite algebras over local rings whose quotient by the radical is a product of copies of the residue field. We define string algebras over local ground rings and recover the notion introduced by Butler and Ringel when the ground ring is a field. We prove they are biserial in a sense of Kiričenko and Kostyukevich. We describe the syzygies of uniserial summands of the radical. We give examples of Bäckström orders that are string algebras over discrete valuation rings.