Ω-Gorenstein Modules over Formal Triangular Matrix Rings

Let A and B be rings and U a ( B ,  A )-bimodule. Under some conditions, Ω -Gorenstein module over the formal triangular matrix ring T = A 0 U B is explicitly described, where Ω is a class of left T -modules. As an application, it is shown that if B U has finite projective dimension and U A has fini...

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Bibliographic Details
Published in:Bulletin of the Malaysian Mathematical Sciences Society 2021-11, Vol.44 (6), p.4357-4366
Main Authors: Wu, Dejun, Yi, Chengang
Format: Article
Language:English
Subjects:
Applications of Mathematics
Mathematics
Mathematics and Statistics
Modules
Rings (mathematics)
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Summary:Let A and B be rings and U a ( B ,  A )-bimodule. Under some conditions, Ω -Gorenstein module over the formal triangular matrix ring T = A 0 U B is explicitly described, where Ω is a class of left T -modules. As an application, it is shown that if B U has finite projective dimension and U A has finite flat dimension, then M = M 1 M 2 φ M is a Gorenstein projective left T -module if and only if M 1 is a Gorenstein projective left A -module, Coker ( φ M ) is a Gorenstein projective left B -module and φ M : U ⊗ A M 1 → M 2 is a monomorphism. This statement covers an earlier result of Enochs, Cortés-Izurdiaga and Torrecillas in this direction.
ISSN:0126-6705
2180-4206
DOI:10.1007/s40840-021-01169-w