The fundamental theorem for coalgebras over the Dedekind ring and application
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Keywords

đối đại số
định lý cơ bản cho các đối đại số
lược đồ nhóm affine phẳng
vành Dedekind coalgebra
the fundamental theorem for coalgebras
flat affine group schemes
Dedekind ring

How to Cite

1.
Nguyễn Đại D. The fundamental theorem for coalgebras over the Dedekind ring and application. hueuni-jns [Internet]. 2022Sep.30 [cited 2024Nov.23];131(1C):47-53. Available from: http://222.255.146.83/index.php/hujos-ns/article/view/6489

Abstract

In this paper, we study the local finiteness of coalgebras, known as the fundamental theorem for coalgebras over the Dedekind ring. First, we give proof of this property for coalgebras which are projective as modules over a principal ideal domain, without using the fundamental theorem for coalgebras over a field. Next, we give a version of the theorem for flat coalgebras over the Dedekind ring that extends the certainty of the theorem over a field. Finally, we apply these results to the coordinate ring of flat affine group schemes.

https://doi.org/10.26459/hueunijns.v131i1C.6489
PDF (Vietnamese)

References

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