Excellent Extensions and Homological Conjectures
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In this paper, we introduce the notion of excellent extensions of rings. Let Γ be an excellent extension of an Artin algebra Λ, we prove that Λ satisfies the Gorenstein symmetry conjecture (resp., finitistic dimension conjecture, Auslander–Gorenstein conjecture, Nakayama conjecture) if and only if so does Γ. As a special case of excellent extensions, when G is a finite group whose order is invertible in Λ acting on Λ and Λ is G-stable, we prove that if the skew group algebra ΛG satisfies strong Nakayama conjecture (resp., generalized Nakayama conjecture), then so does Λ.
1962 ◽
Vol 5
(4)
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pp. 158-159
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1975 ◽
Vol 16
(1)
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pp. 22-28
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2016 ◽
Vol 68
(2)
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pp. 258-279
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2016 ◽
Vol 99
(113)
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pp. 257-264
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2013 ◽
Vol 15
(02)
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pp. 1350004
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2010 ◽
Vol 09
(02)
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pp. 305-314
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