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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.
Mark Johnson, Bernd Ulrich (1996)
Compositio Mathematica
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Eero Hyriy (1993)
Manuscripta mathematica
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C. Năstăsescu, N. Rodinò (1985)
Rendiconti del Seminario Matematico della Università di Padova
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Maurice Auslander, Idun Reiten (1990)
Banach Center Publications
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Claudia Menini (1988)
Rendiconti del Seminario Matematico della Università di Padova
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Refai, Mashhoor, Obiedat, Sofyan (1998)
International Journal of Mathematics and Mathematical Sciences
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W.V. Vasconcelos, S. Morey, S. Noh (1995)
Manuscripta mathematica
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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.
Maria Pia Cavaliere, Gianfranco Niesi (1983)
Manuscripta mathematica
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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.
Samir Mahmoud, S. (1996)
Bulletin of the Belgian Mathematical Society - Simon Stevin
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Santiago Zarzuela (1992)
Publicacions Matemàtiques
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In this note we give a description of a morphism related to the structure of the canonical model of the Rees algebra R(I) of an ideal I in a local ring. As an application we obtain Ikeda's criteria for the Gorensteinness of R(I) and a result of Herzog-Simis-Vasconcelos characterizing when the canonical module of R(I) has the expected form.