Cohen-macaulay and gorenstein artin algebras
WebAug 1, 2024 · The main goal of this paper is to measure the defect of Cohen–Macaulay, Gorenstein, complete intersection and regularity for the tensor product of algebras over a ring. For this sake, we determine the homological invariants which are inherent to these notions, such as the Krull dimension, depth, injective dimension, type and embedding ... WebThe notions of Cohen-Macaulay and Gorenstein rings, as well as Cohen-Macaulay modules, are well established in commutative noetherian ring theory. In [6] we introduced similar notions for artin algebras. This paper is devoted to studying further the module theory of Cohen-Macaulay and Gorenstein artin algebras. As might be expected, …
Cohen-macaulay and gorenstein artin algebras
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WebJun 1, 2005 · We stress that virtually Gorenstein algebras are defined by imposing representation theoretic finiteness conditions on Cohen–Macaulay modules or on modules of virtually finite projective or injective dimension whereas Gorenstein algebras are defined by imposing homological finiteness conditions on the ring. WebJun 1, 2005 · Selfinjective algebras and algebras of finite global dimension are Gorenstein.An artin algebra is called virtually Gorenstein if for a module M, the functor Ext 1 (−, M) vanishes on all ...
WebApr 1, 2001 · Let B be a graded Cohen–Macaulay quotient of a Gorenstein ring, R. It is known that sections of the dual of the canonical module, KB, can be used to construct Gorenstein quotients of R. WebNov 22, 2013 · Beligiannis, A.: Cohen-Macaulay modules (co)torsion pairs and virtually Gorenstein algebras. J. Algebra 288 (1), 137–211 (2005) Article MathSciNet MATH Google Scholar Beligiannis, A.: On algebras of finite Cohen-Macaulay type. Adv. Math. 226 (2), 1973–2024 (2011) Article MathSciNet MATH Google Scholar
WebThis conjecture was initially stated for Artin algebras, and Auslander, Ding and Solberg [1] widened the context to algebras over commutative local rings. A recent result of Huneke and Leuschke [13] establishes the conjecture in the case when R is a quotient by a regular sequence of an excellent Cohen-Macaulay normal domain WebLet A be an Artin-Schelter regular algebra, and let H be a semisimple Hopf algebra which acts on A homogeneously. Under some mild conditions, the invariant subalgebra AH is an Artin-Schelter Gorenstein algebra. The representation, especially the Cohen-Macaulay representations, of AH is one of the main subjects in the noncommutative projective ...
WebOct 18, 2024 · 腾讯ID: 125 959 292. 报告摘要： We recall the definition of the O-operators on bimodules over associative algebras, and we introduce the notions of compatible O-operators and of ON-structures. We show that an ON-structure gives rise to a hierarchy of O-operators and that a solution of the strong Maurer-Cartan equation on the associative ...
WebMay 10, 2013 · On algebras of finite Cohen-Macaulay type. Apostolos Beligiannis. We study Artin algebras and commutative Noetherian complete local rings in connection with the following decomposition property of Gorenstein-projective modules: any Gorenstein-projective module is a direct sum of finitely generated modules. We show that this direct … chinese taipei football leagueWebJan 30, 2010 · Also Cohen-Macaulay finite algebras, having recently been of particular attention ( [5], [7], [11]), are defined in terms of Gorenstein projective modules; recall that an Artin algebra Λ is said ... grandview hollywood condos for saleWebApr 3, 2024 · Finally we give torsion theoretic applications to the structure of Gorenstein and Cohen-Ma,caulay categories, which provide a natural generalization of Gorenstein and Cohen-Macaulay rings. grandview hollow potteryWebGorenstein, Cohen-Macaulay homomorphic image of a Gorenstein local ring and g is P-regular. Proof. Being a homomorphic image of a Gorenstein ring, Q contains an ideal d such ... in the representation theory of Artin algebras. It has generated a significant body of research and has led to the study of several variants and to the formulation of grandview holiday innWebJan 30, 2011 · Finally we study the (stable) relative Auslander algebra of a virtually Gorenstein algebra of finite Cohen–Macaulay type and, under the presence of a cluster tilting object, we give descriptions of the stable category of Gorenstein-projective modules in terms of the cluster category associated to the quiver of the stable relative Auslander … chinese taipei football team rankingWebMay 19, 2016 · Concerning Q3: In QPA one can compute (although I have not tested it extensively) almost split sequences in ⊥ T = { X ∣ Ext Λ i ( X, T) = 0 for i > 0 } for a cotilting module T. When Λ is an admissible quotient of a path algebra and Λ is Gorenstein, then letting T = Λ gives you a way of computing in the category of Cohen-Macaulay modules. chinese taipei gliding sports associationWebIn this thesis we study graded Cohen-Macaulay modules and their possible Hilbert ... for Gorenstein algebras of codimension three and for complete intersections. The motivation for the conjectures comes from the Multiplicity ... On parameter spaces for Artin level algebras. MichiganMath.J.,51(1):187–207,2003. grandview hollywood condo