On the vanishing of Ext over formal triangular matrix rings

DOI10.1515/FORUM.2006.048zbMath1148.16006OpenAlexW1968741036MaRDI QIDQ3425521

Javad Asadollahi, Shokrollah Salarian

Publication date: 26 February 2007

Published in: Forum Mathematicum (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/forum.2006.048

zbMATH Keywords

tilting modulesprojective dimensionflat coverscotilting modulesinjective dimensioncotorsion modulesGorenstein injective modulesGorenstein projective modulestriangular matrix rings

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) Module categories in associative algebras (16D90) Homological functors on modules (Tor, Ext, etc.) in associative algebras (16E30) Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.) (16E65) Homological dimension in associative algebras (16E10)

Related Items (19)

Silting and cosilting modules over trivial ring extensions ⋮ Frobenius categories over a triangular matrix ring and comma categories ⋮ Homological dimensions of special modules over formal triangular matrix rings ⋮ Representation dimension via tilting theory ⋮ Modules over formal matrix rings. ⋮ Injective cogenerators, cotilting modules and cosilting modules ⋮ Gorenstein complexes over formal triangular matrix rings ⋮ Gorenstein conditions over triangular matrix rings ⋮ Duality pairs and FP-injective modules over formal triangular matrix rings ⋮ Unnamed Item ⋮ Gorenstein homological dimensions of modules over triangular matrix rings ⋮ Flat covers over formal triangular matrix rings and minimal Quillen factorizations ⋮ \( \Omega \)-Gorenstein modules over formal triangular matrix rings ⋮ Homological dimension formulas for trivial extension algebras ⋮ Recollements of stable categories of Gorenstein injective modules ⋮ Cotorsion pairs and approximation classes over formal triangular matrix rings ⋮ When the Schur functor induces a triangle-equivalence between Gorenstein defect categories ⋮ Gorenstein flat modules and dimensions over formal triangular matrix rings ⋮ Homological aspects of formal triangular matrix rings

Cites Work

• Tilting modules of finite projective dimension
• Injective and flat covers, envelopes and resolvents
• Tilting modules and tilting torsion theories
• Study of modules over formal triangular matrix rings
• Rings of quotients of generalized matrix rings
• Balanced Subgroups of Abelian Groups
• Resolutions by gorenstein injective andprojective modules and modules of finite injective dimension overgorenstein rings
• Partial cotilting modules and the lattices induced by them
• Tilting modules and ∗-modules
• Study of formal triangular matrix rings
• Tilting preenvelopes and cotilting precovers

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