On Artin Algebras Arising from Morita Contexts
By Edward L. Green, Chrysostomos Psaroudakis. 2013
65 citations recorded by the source corpus.
We study Morita rings Λ(ϕ,ψ)=AANBBMAB$\Lambda _{(\phi ,\psi )}=\left (\begin {array}{cc}A &_{A}N_{B} \\ _{B}M_{A} & B \end {array}\right )$ in the context of Artin algebras from various perspectives. First we study covariantly finite, contravariantly finite, and functorially finite subcategories of the module category of a Morita ring when the bimodule homomorphisms ϕ$\phi $ and ψ$\psi $ are zero. Further we give bounds for the global dimension of a Morita ring Λ(0,0)$\Lambda _{(0,0)}$, as an Artin algebra, in terms of the global dimensions of A and B in the case when both ϕ$\phi $ and ψ$\psi $ are zero. We illustrate our bounds with some examples. Finally we investigate when a Morita ring is a Gorenstein Artin algebra and then we determine all the Gorenstein-projective modules over the Morita ring Λϕ,ψ$\Lambda _{\phi ,\psi }$ in case A=N=M=B$A=N=M=B$ and A an Artin algebra.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/5b998b2d9aece30a70fdb0cf19d38216f54ba60c
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In Algebra and Number Theory
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Gorenstein Homological Aspects of Monomorphism Categories via Morita Rings (2015, methodology): “Let Λ(0,0) be a Morita ring such that ANB has an A-tight projective Λ(0,0)-resolution and BMA has a B-tight projective Λ(0,0)-resolution, in the sense of [25].”