非结合与 hom-结合 Ore 扩张的 Hilbert 基定理
环与代数
2025-07-16 v8
摘要
我们证明了 Hilbert 基定理的一个 hom-结合版本，它作为特例包含了非结合版本以及经典的关于 Ore 扩张的结合型 Hilbert 基定理。在此过程中，我们发展了 hom-模理论。最后我们给出一些非结合与 hom-结合 Ore 扩张的例子，由我们的定理可知它们均为诺特环。
引用
@article{arxiv.1804.11304,
title = {Hilbert's basis theorem for non-associative and hom-associative Ore extensions},
author = {Per Bäck and Johan Richter},
journal= {arXiv preprint arXiv:1804.11304},
year = {2025}
}
备注
18 pages; simplified the proof of Proposition 12; changed the title, abstract and introduction, added an example and a corollary together with some minor changes; corrected some minor typos in reference list; major revision including new title, shorter proofs and four new examples; added an example and updated an example, adjusted the language; added/adjusted examples; minor update