The stable module category of a general ring

Author: mrcp

August undefined, 2024

WebIn , abelian model categories were used to introduce the stable module category of a general ring. And in [ 5 , 31 ], there appeared an elegant connection between abelian model categories and recollements of triangulated categories. WebOne important property of the stable module category is it allows defining the Ω functor for general rings. When R is perfect (or M is finitely generated and R is semiperfect), then …

AC-GORENSTEIN RINGS AND THEIR STABLE …

WebJun 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 … THE STABLE MODULE CATEGORY OF A GENERAL RING DANIEL BRAVO, JAMES … john wooden center classes

Stable model categories are categories of modules - uni …

WebJun 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 … WebMay 22, 2014 · The stable module category of a general ring D. Bravo, James Gillespie, Mark Hovey Published 22 May 2014 Mathematics arXiv: Rings and Algebras For any ring … 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 john wooden award candidates

[1405.5768v1] The stable module category of a general ring

arXiv:1405.5768v1 [math.RA] 22 May 2014

http://homepages.math.uic.edu/~bshipley/hovey.pdf how to heal an intercostal muscle strainWebThe stable module category of a ﬁnite group G over a ﬁeld k is a basic object of study in modular representation theory; it is a triangulated cate-gory because injective and projective k[G]-modules coincide. Cotorsion pairs can be used to construct two diﬀerent model structures on the category of how to heal an inguinal hernia naturally

"WebJan 18, 2024 · The stable module category of a general ring. arXiv:1405.5768 Christensen, L., Frankild, A., Holm, H.: On Gorenstein projective, injective, and flat modules. A functorial description with applications. J. Algebra 302 (1), 231–279 (2006) Article MathSciNet MATH Google Scholar Enochs, E.E., Jenda, O.M.G.: Relative Homological Algebra. " - The stable module category of a general ring

The stable module category of a general ring

$arXiv:1405.5768v1 [math.RA] 22 May 2014$

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 … http://homepages.math.uic.edu/~bshipley/classTopFinal.pdf

Did you know?

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. WebSep 23, 2024 · In representation theory, the stable module category is a category in which projectives are factored out. Let R be a ring. For two modules M and N, define H o m ( M , N ) to be the set of Rlinear maps from M to N modulo the relation that fg if fg factors through a projective module. The s

WebTHE STABLE MODULE CATEGORY OF A GENERAL RING 3 AC-acyclic if it is exact and Hom(I,X) remains exact for any absolutely clean module I. This is our generalization of … 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 …

WebSo 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 … 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 …

Webin some cases their stable (graded) module categories are recovering D(R), the derived category of the ring R. 2.Preliminaries Throughout the paper R denotes a general ring with identity. We will work with both left and right R-modules. But we will favor the left, so that R-module will mean left R-module, unless stated otherwise.

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. john wooden assistant coachesWebGivenan 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 … john wooden citizenship cupWebAug 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 … how to heal an injured hamstringWebThe 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: how to heal a nipple piercingWebThe stable module category of a general ring Citing article May 2014 arXiv Daniel Bravo James Gillespie Mark Hovey View full-text ... The main result of this paper is a model categorical analogue... john wooden award finalists 2014WebThe stable module category of a general ring (arXiv:1405.5768). [Google Scholar]], showing that they are the fibrant objects of a cofibrantly generated model structure on 풢. … how to heal an iron golem minecraftWebOne 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) … john wooden classic scores