Auslander-gorenstein rings

Ajitabh, Kaushal; Smith, S. Paul; Zhang, J.J.

doi:10.1080/00927879808826267

Cited by 49 publications

(35 citation statements)

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“…Since J := I H R is the Jacobson radical of R, J is the unique maximal right and left ideal of R. But now JT = I H · OG · T = I H,G T is the Jacobson radical of T so JT = T. Hence T is a faithfully flat R-module by [18,Proposition 7.2.3]. [8,Corollary 1.3] because T is Auslander-Gorenstein, and we have seen above that gld(T) ≤ dim H. The result follows.…”

Section: Lemma Oh H → Og H and Og H Is A Faithfully Flat Oh H -Modulementioning

confidence: 99%

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Localisation at Augmentation Ideals in Iwasawa Algebras

Ardakov¹

2006

Glasgow Math. J.

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Abstract. Let G be a compact p-adic analytic group and let G be its completed group algebra with coefficient ring the p-adic integers ‫ޚ‬ p . We show that the augmentation ideal in G of a closed normal subgroup H of G is localisable if and only if H is finite-by-nilpotent, answering a question of Sujatha. The localisations are shown to be Auslander-regular rings with Krull and global dimensions equal to dim H. It is also shown that the minimal prime ideals and the prime radical of the ‫ކ‬ p -version G of G are controlled by + , where + is the largest finite normal subgroup of G. Finally, we prove a conjecture of Ardakov and Brown [1].

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Section: Lemma Oh H → Og H and Og H Is A Faithfully Flat Oh H -Modulementioning

confidence: 99%

“…The method of proof is unusual in that the global dimension gld( G,H ) and the Krull dimension K( G,H ) are computed simultaneously. The crucial fact used here is a result of Roos [8,Corollary 1.3] which ensures that K(T) ≤ gld(T) for any Auslander-regular ring T.…”

Section: Theorem B Suppose That H/ + (H) Is Nilpotent Then (A) Gh mentioning

confidence: 99%

Localisation at Augmentation Ideals in Iwasawa Algebras

Ardakov¹

2006

Glasgow Math. J.

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“…The hypothesis (*) in [AjSZ,Theorem 6.1] holds trivially since H is Cohen-Macaulay with respective to GK-dimension.…”

Section: (B) By Part (A) We Have Extmentioning

confidence: 93%

Hopf algebras with rigid dualizing complexes

Zhang

2008

Isr. J. Math.

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Let H be a Hopf algebra over a base field. If H has an N-filtration such that the associated graded ring is connected graded noetherian and has enough normal elements, then H is Gorenstein. This gives a partial solution to a question of Brown and Brown-Goodearl. As a consequence, every quotient Hopf algebra of a generic quantized coordinate ring of a connected semisimple Lie group is Auslander-Gorenstein and Cohen-Macaulay. The last statement answers a question of Goodearl-Zhang.

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“…This is straightforward. 2 Since this paper was first written Ken Brown has pointed out that this last proposition is a special case of general duality results for Auslander-Gorenstein rings that can be found in [1].…”

Section: Definitionmentioning

confidence: 94%

Homogeneity and rigidity of the Brookes–Groves invariant for the non-commutative torus

Wadsley¹

2006

Journal of Algebra

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Auslander-gorenstein rings

Cited by 49 publications

References 11 publications

Localisation at Augmentation Ideals in Iwasawa Algebras

Localisation at Augmentation Ideals in Iwasawa Algebras

Hopf algebras with rigid dualizing complexes

Homogeneity and rigidity of the Brookes–Groves invariant for the non-commutative torus

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