On the relative homology of cleft extensions of rings and abelian categories

DOI10.1016/S0022-4049(99)00091-2zbMath0979.18007WikidataQ126591825 ScholiaQ126591825MaRDI QIDQ1577504

Apostolos Beligiannis

Publication date: 4 September 2000

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

zbMATH Keywords

Gorenstein ringpolynomial ringperfect ringscleft extensionhomological dimensionrelative homologytilting moduletrivial extensionstriangular matrix ringsabelian categoriesfree ringexterior ringsymmetric ring

Mathematics Subject Classification ID

Free, projective, and flat modules and ideals in associative algebras (16D40) Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.) (16E65) Resolutions; derived functors (category-theoretic aspects) (18G10) Projectives and injectives (category-theoretic aspects) (18G05) Homological dimension (category-theoretic aspects) (18G20) Abelian categories, Grothendieck categories (18E10) Relative homological algebra, projective classes (category-theoretic aspects) (18G25) Homological dimension in associative algebras (16E10) Extensions of associative rings by ideals (16S70)

Related Items (8)

Gorenstein homological aspects of monomorphism categories via Morita rings ⋮ Recollements induced by left Frobenius pairs ⋮ On Artin algebras arising from Morita contexts. ⋮ Cyclic homology of cleft extensions of algebras ⋮ Hochschild cohomology of algebras arising from categories and from bounded quivers ⋮ Deleting or adding arrows of a bound quiver algebra and Hochschild (co)homology ⋮ Reduction techniques for the finitistic dimension ⋮ Homological Dimensions of Extensions of Artinian Rings by Right Projective Bimodules

Cites Work

• On the derived category of a finite-dimensional algebra
• Integrations and cohomology theory
• Tilting modules of finite projective dimension
• Notes on the no loops conjecture
• Trivial extensions of Abelian categories. Homological algebra of trivial extensions of Abelian categories with applications to ring theory
• On extensions of abelian categories with applications to ring theory
• Extensions of abelian categories and the strong no-loops conjecture
• Semiprimary rings of generalized triangular type
• Inertial subalgebras of complete algebras
• Explicit formulae for the global homological dimensions of trivial extensions of rings
• Algebras of cohomologically finite dimension
• On the cohomology groups of an associative algebra
• Finitistic Dimension and a Homological Generalization of Semi-Primary Rings
• Classes of extensions and resolutions
• A complete characterization of weak inertial coefficient rings
• The Structure of Schur Algebras S_k(n, p) for n ≥ p
• Higher algebraic K-theory: I
• The global homological dimension of semi-trival extensions of rings.
• Cleft extensions of abelian categories and applications to ring theory
• Algebra Extensions and Nonsingularity
• Foundations of relative homological algebra
• Inertial Subalgebras of Algebras Over Commutative Rings
• Des catégories abéliennes
• Cleft Rings
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• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
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