On the injective dimension of the Jacobson radical
Rene Marczinzik
TL;DR
This paper explores the relationship between the injective dimension of the Jacobson radical and the global dimension in Artin algebras, providing proofs in specific cases.
Contribution
It proves the conjecture that the injective dimension of the Jacobson radical equals the global dimension for certain classes of Artin algebras.
Findings
Confirmed the conjecture for algebras with finite global dimension
Extended proof to some additional cases
Established a link between injective and global dimensions in Artin algebras
Abstract
We conjecture that the injective dimension of the Jacobson radical equals the global dimension for Artin algebras. We provide a proof of this conjecture in case the Artin algebra has finite global dimension and in some other cases.
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