Cotilting module
WebTILTING, COTILTING, AND SPECTRA OF NOETHERIAN RINGS 3491 Proof. This is easily obtained fromLemma 1.4(i) by induction on .Wealsouse the fact that Ass j(P) ⊆ Ass j(R) for any j ∈ Z and any projective module P. We finish by recalling a well-known property of the residue field considered as anR-module(seee.g.[23,Theorem18.4]),anditsconsequences:
Cotilting module
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WebJul 1, 2024 · One can also consider the dual notion of cotilting modules. Tilting theory goes back to the work of I.N. Bernshtein, I.M. Gel'fand and V.A. Ponomarev on the characterization of representation-finite hereditary algebras through their ordinary quivers … WebClassical tilting theory generalizes Morita theory of equivalence of module cat-egories. The key property – existence of category equivalences between large fullsubcategories of the module categories – forces the representing tilting module tobe finitely generated.However, some aspects of the classical theory can be extended to infinitely …
WebAug 1, 2024 · When Λ is an artin algebra and T is a cotilting Λ-module, the functor HomΛ(, T) induces a duality between certain subcategories of the finitely generated modules over Λ and EndΛ(T). The ... WebDec 2, 2009 · Some examples and characterizations of Tor-tilting modules are given.Among others, it is shown that U R is Tor-tilting if and only if U + is cotilting. Moreover, both …
WebApr 28, 2009 · ABSTRACT. Let R be an artin algebra. We prove that a tilting R -module ω is cotilting if and only if every finitely generated R -module has finite ω -Gorenstein resolution dimension and that a cotilting R -module ω is tilting if and only if every finitely generated R -module has finite ω -Gorenstein coresolution dimension. WebDec 2, 2009 · Some examples and characterizations of Tor-tilting modules are given.Among others, it is shown that U R is Tor-tilting if and only if U + is cotilting. Moreover, both tilting modules and completely faithful flat modules are proved to be Tor-tilting.The torsion theory induced by a Tor-tilting module is also investigated.
WebOn faithfully balanced modules, F-cotilting and F-Auslander algebras. Ma, Biao. ; Sauter, Julia. We revisit faithfully balanced modules. These are faithful modules having the double centralizer property. For finite-dimensional algebras our main tool is the category $ {\rm cogen}^1 (M)$ of modules with a copresentation by summands of finite sums ...
Webd of the family of finite A-module complexes with fixed sequence d of dimensions and an “almost projective” complex X ∈ CompA d, there exists a canonical vector space embedding TX(Comp A d)/TX(G.X) −→ HomDb(A-Mod) (X,X[1]), where G is the pertinent product of general linear groups acting on CompA d, tangent spaces freshsecWebstratified algebras for which the characteristic tilting and cotilting modules coincide ... father and son wedding songWebAug 12, 2009 · Equivalence and Duality for Module Categories with Tilting and Cotilting for Rings - March 2004 Skip to main content Accessibility help We use cookies to distinguish you from other users and to provide you with a better experience on our websites. fresh seaweed grapesWebAlmost complete cotilting modules are studied in [8], [9] and [10]. The following theorem is contained is these papers. Theorem 3.1. Let M be an almost complete cotilting module over an artin ... father and son wegbergWebThe theory concerning dualizing modules and cotilting modules has been regularly studied in the literature, for example, in [2, 4, 5, 14, 15]. In particular, Auslander and Reiten [4] define a Cohen–Macaulay Artin algebra and show that a Cohen– Macaulay Artin algebra has a dualizing module, and vice versa. Let be an Artin algebra. fresh seaweed for sale ukWebApr 1, 2001 · Dualizing a result of Bongartz, we show that a module P is partial cotilting iff P is a direct summand of a cotilting module C such that the left Ext-orthogonal class ⊥P … father and son weekend getaways californiaWebNov 1, 2015 · We show that every injective homological ring epimorphism f: R → S where S R has flat dimension at most one gives rise to a 1-cotilting R-module and we give … fresh seaweed in tomato pot