منابع مشابه
Homological properties of rings of functional-analytic type.
Strong flatness properties are established for a large class of functional-analytic rings including all C*-algebras. This is later used to prove that all those rings satisfy excision in Hochschild and in cyclic homology over almost arbitrary rings of coefficients and that, for stable C*-algebras, the Hochschild and cyclic homology groups defined over an arbitrary coefficient ring k subset C of ...
متن کاملHomological Properties of Quantized Coordinate Rings of Semisimple Groups
We prove that the generic quantized coordinate ringOq(G) is Auslander-regular, Cohen-Macaulay, and catenary for every connected semisimple Lie group G. This answers questions raised by Brown, Lenagan, and the first author. We also prove that under certain hypotheses concerning the existence of normal elements, a noetherian Hopf algebra is Auslander-Gorenstein and Cohen-Macaulay. This provides a...
متن کاملHomological Dimensions and Regular Rings
A question of Avramov and Foxby concerning injective dimension of complexes is settled in the affirmative for the class of noetherian rings. A key step in the proof is to recast the problem on hand into one about the homotopy category of complexes of injective modules. Analogous results for flat dimension and projective dimension are also established.
متن کاملHomological Characterizations of Rings with Property (P)
A commutative ring R is said to satisfy property (P) if every finitely generated proper ideal of R admits a non-zero annihilator. In this paper we give some necessary and sufficient conditions that a ring satisfies property (P). In particular, we characterize coherent rings, noetherian rings and P-coherent rings with property (P).
متن کاملGorenstein Homological Dimensions of Commutative Rings
The classical global and weak dimensions of rings play an important role in the theory of rings and have a great impact on homological and commutative algebra. In this paper, we define and study the Gorenstein homological dimensions of commutative rings (Gorenstein projective, injective, and flat dimensions of rings) which introduce a new theory similar to the one of the classical homological d...
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 1997
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700033992