An analogue of Serre’s conjecture for a ring of distributions
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AbstractThe set 𝒜 := δ0+ 𝒟+′, obtained by attaching the identity δ0 to the set 𝒟+′ of all distributions on with support contained in (0, ∞), forms an algebra with the operations of addition, convolution, multiplication by complex scalars. It is shown that 𝒜 is a Hermite ring, that is, every finitely generated stably free 𝒜-module is free, or equivalently, every tall left-invertible matrix with entries from 𝒜 can be completed to a square matrix with entries from 𝒜, which is invertible.
1974 ◽
Vol 26
(6)
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pp. 1380-1383
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2010 ◽
Vol 5
(1)
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pp. 103-125
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2005 ◽
pp. 87-103
2014 ◽
Vol 14
(3)
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pp. 639-672
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