分布环的Serre猜想的一个类比

Q3 Mathematics

Topological Algebra and its Applications Pub Date : 2020-01-01 DOI:10.1515/taa-2020-0100

A. Sasane

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引用次数: 0

摘要

在(0，∞)的支持下，将等式δ0附加到𝕉上所有分布的集合的λ + '上，得到一个集:=𝔺δ0+ + '，用复数标量进行加法、卷积、乘法运算，形成一个代数。证明了它是一个Hermite环，即每一个有限生成的稳定自由的𝒜-module都是自由的，或者等价地，每一个高的左可逆的矩阵都可以被补成一个包含有等式的平方矩阵，它是可逆的。

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An analogue of Serre’s conjecture for a ring of distributions

Abstract The 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.

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来源期刊

Topological Algebra and its Applications Mathematics-Algebra and Number Theory

CiteScore

1.20

自引率

0.00%

发文量

审稿时长

24 weeks