Methods of Graded Rings

Năstăsescu, C.; Oystaeyen, Freddy Van

doi:10.1007/b94904

Cited by 355 publications

(468 citation statements)

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“…The first part and the first claim in the second part of the proposition are obvious. The reference for the last statement is Theorem 4.4.4(v) in [38]; see also Theorems 4.4.6 and 9.6.8 in [38].…”

Section: Proposition 212 a Simple R(ν)-module S Is Finite-dimensionmentioning

confidence: 99%

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A diagrammatic approach to categorification of quantum groups I

2009

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Section: Proposition 212 a Simple R(ν)-module S Is Finite-dimensionmentioning

confidence: 99%

“…We thank J. Brundan and A. Kleshchev for pointing out reference [38] to us. This paper was written while the first author was at the Institute for Advanced Study, and he would like to thank the Institute for its hospitality and the NSF for fully supporting him during that time through the grant DMS-0635607.…”

Section: Acknowledgmentsmentioning

confidence: 99%

A diagrammatic approach to categorification of quantum groups I

2009

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“…Castaño-Iglesias, in [7], gives an example of a pair of right adjoint contravariant functors between the categories of all G-graded unital right R-modules and of all G-graded unital left S-modules, where G is a group and R and S are two G-graded unital rings (see also [13]). Other examples of such pairs of functors could be found in [14].…”

Section: Preliminariesmentioning

confidence: 99%

Coplexes in abelian categories

Pop

2017

Stud. Univ. Babes-Bolyai Math.

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Abstract. Starting with a pair F : A B : G of additive contravariant functors which are adjoint on the right, between abelian categories, and with a class U, we define the notion of (F, U)-coplex. Considering a reflexive object U of A with F(U ) = V projective object in B, we construct a natural duality between the category of all (F, add(U ))-coplexes in A and the subcategory of B consisting in all objects in B which admit a projective resolution with all terms in the class add(V ).Mathematics Subject Classification (2010): 16E30, 16D90.

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“…We record the following well known lemma, which can be found for instance in [NV,Corollary 2.4.4]. We shall often use it without explicit mention.…”

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confidence: 99%

“…In particular l.f.Λ contains the finitely generated projective modules and the finitely cogenerated graded injective modules. The graded injective modules are not necessarily injective as ungraded modules [NV,Remark 2.3.3]. We have the following duality result, a reference for which is [M].…”

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confidence: 99%