2024 The stable module category of a general ring

The stable module category of a general ring

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WebThe stable module category of a general ring (arXiv:1405.5768). [Google Scholar]], Daniel Bravo and Mark Hovey. The original idea of this paper was simply to generalize some of the results of that paper to a more general setting. To this end, the paper started as notes in the Summer of 2014 while preparing the talk [12Gillespie, J.(2014). WebMar 16, 2024 · the stable module category for groups of type Φ, as the largest quotient of the category of modules on which the syzygy functor is invertible [35]. This category is equipped with a triangulated structure compatible with the tensor product over the ground ring. In other words, it is a tensor triangulated category in the language of Balmer [2].

n G arXiv:1512.01716v1 [math.RT] 6 Dec 2015

WebAug 15, 2016 · Having an issue? Is data on this page outdated, violates copyrights or anything else? Report the problem now and we will take corresponding actions after … WebFor any ring R we construct two triangulated categories, each admitting a functor from R-modules that sends projective and injective modules to 0. When R is a quasi-Frobenius or … free wildlife wood burning patterns

Absolutely Clean, Level, and Gorenstein AC-Injective Complexes

WebAug 1, 2024 · For a general R, the AC-Gorenstein homological algebra of Bravo–Gillespie–Hovey is the one coming from the duality pair where is the class of level R -modules and is class of absolutely clean R -modules. Indeed we show here that the work in [1] can be extended to obtain similar abelian model structures on -Mod from any a … WebGivenan E∞-ring spectrum R, a general theme is that the Picard group will be easier to understand if the homotopy groups of Rare homologically simple. ... TORUS ACTIONS ON STABLE MODULE CATEGORIES, PICARD GROUPS, AND LOCALIZING SUBCATEGORIES3 Theorem 1.3. If Gis an abelian p-group of rank n, then one can construct an action of the n … WebAug 1, 2024 · 3. The Gorenstein flat model structure. Let R be a right coherent ring and R -Mod the category of left R -modules. Our goal is to apply Theorem 2.1 to obtain a … free wildtangent bubble shooter game

Gorenstein Projective Precovers SpringerLink

WebMay 31, 2024 · Abstract. In the paper, Ding projective modules and Ding projective complexes are considered. In particular, it is proven that Ding projective complexes are precisely the complexes X for which each Xm is a Ding projective R -module for all m ∈ ℤ. Download to read the full article text. WebFeb 3, 2024 · Idea Basic idea. The basic idea is that a module V V is an object equipped with an action by a monoid A A.This is closely related to the concept of a representation of a group.. A familiar example of a module is a vector space V V over a field k k: this is a module over k k in the category Ab of abelian groups: every element in k k acts on the vector … fashion marketing salary londonWebThe stable module category is defined by setting the objects to be the R -modules, and the morphisms are the equivalence classes Hom ― ( M, N) . Given a module M, let P be a … fashion marketing salary nyc

"WebAug 18, 2024 · As an application, a new description of the classical singularity category $$\mathbb {D} _\mathrm{{sg}}(R)$$ is given. The relative singularity categories are applied to lift a stable equivalence between two suitable subcategories of the module categories of two given right noetherian rings to get a singular equivalence between the rings. " - The stable module category of a general ring

The stable module category of a general ring

WebLet R be a ring (not necessarily commutative) and ( ℒ, 𝒜) a bi-complete duality pair. We investigate the notions of (flat-typed) ( ℒ, 𝒜) -Gorenstein rings, which unify Iwanaga–Gorenstein rings, Ding–Chen rings, AC-Gorenstein rings and Gorenstein n … WebMay 22, 2014 · Our stable module categories are homotopy categories of Quillen model structures on the category of R-modules. These model categories involve generalizations …

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THE STABLE MODULE CATEGORY OF A GENERAL RING DANIEL BRAVO, JAMES … WebJun 26, 2015 · Let $\underline{\text{mod-}R}$ be the stable module category, with the... Stack Exchange Network Stack Exchange network consists of 181 Q&A communities including Stack Overflow , the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Webhomotopy category of all chain complexes of injective R-modules, is a compactly generated triangulated category whenever R is a coherent ring [Sto14]. In [BGH13], abelian model categories were used to introduce the stable module category of a general ring. And in [Bec14, Gil12], there appeared an elegant connection between WebThe stable module category of a general ring. D Bravo, J Gillespie, M Hovey. arXiv preprint arXiv:1405.5768, 2014. 114: 2014: Model structures on exact categories. ... The flat stable module category of a coherent ring. J Gillespie. Journal of Pure and Applied Algebra 221 (8), 2025-2031, 2024. 24:

WebOct 24, 2024 · Define the stable category of right A -modules mod _ − A as a category with objects the finitely generated modules over A and Hom mod _ − A ( M, N) = Hom mod − A ( M, N) / P ( M, N), where P ( M, N) is the subgroup of morphisms which factor through a projective module, so f ∈ P ( M, N) if and only if there is a projective finitely generated … WebOur stable module categories are homotopy categories of Quillen model structures on the category of R-modules. These model categories involve generalizations of Gorenstein …

WebSep 1, 2015 · Throughout the paper, a ring will always be an associative ring with identity, and a module a left module. Given a ring, the corresponding stable module category has …

Webequivalences between module categories in terms of bimodules, see e.g. [1, Thm. 22.1]. In The-orem 4.1.2 we present an analogous result which explains how a chain of Quillen … fashion marketing salary in new yorkWebJun 1, 2016 · On the other hand, as an attempt to generalize the theory to arbitrary groups, Tate–Vogel cohomology (also known as stable cohomology in [9] to emphasize a relation to stabilization of module categories) was developed independently by Mislin [49], Benson and Carlson [14] and Vogel (first published account in [34]) and extended to complexes by … fashion marketing strategy templateWebOne important property of the stable module category is it allows defining the Ω functor for general rings. When Ris perfect(or Mis finitely generatedand Ris semiperfect), then Ω(M) … fashion marketing school new yorkWebJun 1, 2024 · The stable module category of a general ring Kenneth S. Brown Homological criteria for finiteness Comment. Math. Helv. (1975) Kenneth S. Brown Cohomology of Groups (1994) Jianlong Chen et al. On n -coherent rings Commun. Algebra (1996) D.L. Costa Parameterizing families of non-Noetherian rings Commun. Algebra (1994) David E. Dobbs … fashion market lavora con noiWebSo a $0$-coherent AC-Gorenstein ring is precisely a usual Gorenstein ring in the sense of Iwanaga, while a $1$-coherent AC-Gorenstein ring is precisely a Ding–Chen ring. We show … fashion marketing schools in new yorkhttp://homepages.math.uic.edu/~bshipley/classTopFinal.pdf fashion marketing trendWebApr 25, 2016 · Absolutely clean and level R -modules were introduced in [ 2] and used to show how Gorenstein homological algebra can be extended to an arbitrary ring R. This led to the notion of Gorenstein AC-injective and Gorenstein AC-projective R -modules. Here we study these concepts in the category of chain complexes of R -modules. fashion marketing vs fashion merchandising