每一个有限生成的阿贝尔群都是一个广义聚类代数的类群

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra Pub Date : 2025-09-03 DOI:10.1016/j.jalgebra.2025.08.017

Mara Pompili

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引用次数: 0

摘要

我们确定了具有Krull域的广义簇代数的类群。特别是，这为确定广义聚类代数是否是UFD提供了一个标准。实际上，任何有限生成的阿贝尔群都可以被实现为广义聚类代数的类群。此外，我们还证明了广义簇代数是ff -域，它们的簇变量是强原子。最后，我们研究了劳伦现象代数的因式分解和环论性质。

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Every finitely generated abelian group is the class group of a generalized cluster algebra

We determine the class group of those generalized cluster algebras that are Krull domains. In particular, this provides a criterion for determining whether or not a generalized cluster algebra is a UFD. In fact, any finitely generated abelian group can be realized as the class group of a generalized cluster algebra. Additionally, we show that generalized cluster algebras are FF-domains and that their cluster variables are strong atoms. Finally, we examine the factorization and ring-theoretic properties of Laurent phenomenon algebras.

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来源期刊

Journal of Algebra 数学-数学

CiteScore

1.50

自引率

22.20%

发文量

414

审稿时长

2-4 weeks

期刊介绍： The Journal of Algebra is a leading international journal and publishes papers that demonstrate high quality research results in algebra and related computational aspects. Only the very best and most interesting papers are to be considered for publication in the journal. With this in mind, it is important that the contribution offer a substantial result that will have a lasting effect upon the field. The journal also seeks work that presents innovative techniques that offer promising results for future research.