Some constructions over graded rings: Applications

DOI10.1016/0021-8693(89)90192-0zbMath0678.16001OpenAlexW2072649652MaRDI QIDQ1123958

Constantin Năstăsescu

Publication date: 1989

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-8693(89)90192-0

zbMATH Keywords

graded modulesquotient categoryadjunctionslocalizing subcategoryequivalence of categoriesstrongly gradedinduced functorcoinduced functorG- graded ringsgr-injective envelopegr-injective moduleshomogeneous component functorssuspension functors

Mathematics Subject Classification ID

Injective modules, self-injective associative rings (16D50) Module categories in associative algebras (16D90) Category-theoretic methods and results in associative algebras (except as in 16D90) (16B50) Graded rings and modules (associative rings and algebras) (16W50) Localization and associative Noetherian rings (16P50)

Related Items (29)

Coinduction for semigroup-graded rings ⋮ Injective modules graded by g-sets ⋮ BLOCK THEORY FOR GROTHENDIECK CATEGORIES: APPLICATIONS ⋮ Topological aspects of graded rings ⋮ GRADED TRIANGULAR EXTENSIONS OVER A RING ⋮ $n$-${\rm gr}$-coherent rings and Gorenstein graded modules ⋮ Relative injective covers ⋮ When is hom_R(M,−) equal to hom_R(M,−) in the category R-gr? ⋮ Modules graded by \(G\)-sets: Duality and finiteness conditions ⋮ The coinduced functor for infinite dimensional Hopf algebras ⋮ Gradings of finite support. Application to injective objects ⋮ Induction functors and stable Clifford theory for Hopf modules ⋮ Graded rings and equivalences of categories ⋮ Preserving and reflecting covers by functors. Applications to graded modules ⋮ Category of $n$-FCP-gr-projective modules with respect to special copresented graded modules ⋮ Wide morita contexts ⋮ Coinduction functor and simple comodules. ⋮ Quotient rings of graded associative rings. I. ⋮ Semigroup-graded rings with finite support ⋮ Singularity categories of representations of algebras over local rings ⋮ Relative projectivity, graded Clifford theory, and applications ⋮ On certain properties and invariants of graded rings and modules ⋮ Gorenstein GR-injective and GR-projective modules ⋮ On graded selfduality ⋮ Graded quotient rings ⋮ $n$-strongly Gorenstein graded modules ⋮ Isomorphisms of graded endomorphism rings of graded modules close to free ones. ⋮ Graded t-rings with finite support ⋮ Maschke functors, semisimple functors and separable functors of the second kind: applications

Cites Work

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• Group rings of graded rings. Applications
• When is R-gr equivalent to the category of modules?
• Group-graded rings and modules
• Prime ideals in crossed products of finite groups
• Modules with decompositions that complement direct summands
• Finitely graded rings, morita duality and self-injectivity
• Group-Graded Rings, Smash Products, and Group Actions
• Group graded rings
• Strongly Graded Rings of Finite Groups
• Clifford theory for group-graded rings.
• Des catégories abéliennes

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