Displaying similar documents to “One-Dimensional Local Rings with Reduced Associated Graded Ring and Their Hilbert Functions.”

Construction of Auslander-Gorenstein local rings as Frobenius extensions

Mitsuo Hoshino, Noritsugu Kameyama, Hirotaka Koga (2015)

Colloquium Mathematicae

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Starting from an arbitrary ring R we provide a systematic construction of ℤ/nℤ-graded rings A which are Frobenius extensions of R, and show that under mild assumptions, A is an Auslander-Gorenstein local ring if and only if so is R.

Recognizing dualizing complexes

Peter Jørgensen (2003)

Fundamenta Mathematicae

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Let A be a noetherian local commutative ring and let M be a suitable complex of A-modules. It is proved that M is a dualizing complex for A if and only if the trivial extension A ⋉ M is a Gorenstein differential graded algebra. As a corollary, A has a dualizing complex if and only if it is a quotient of a Gorenstein local differential graded algebra.

Weak dimension of group-graded rings.

Angel del Río (1990)

Publicacions Matemàtiques

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We study the weak dimension of a group-graded ring using methods developed in [B1], [Q] and [R]. We prove that if R is a G-graded ring with G locally finite and the order of every subgroup of G is invertible in R, then the graded weak dimension of R is equal to the ungraded one.