内态环为 V 环的阿贝尔群

IF 0.5 3区数学 Q3 MATHEMATICS

Journal of Algebra and Its Applications Pub Date : 2024-06-04 DOI:10.1142/s0219498825502871

Afshin Amini, Babak Amini, Ehsan Momtahan

引用次数: 0

摘要

我们研究的是其内定环是 V 环的无边群。让 G 是一个非还原的阿贝尔群，我们证明，当且仅当 G=B⊕ℚn 时，End(G) 的任一边都是一个 V 环，其中 B 是一个驯服的基本阿贝尔群。我们注意到，一个还原群的内形是一个 V 环，它是一个 sp 群。认识到 End(G) 也是∏p∈ℙEnd(Gp) 的一个 sp 群，我们证明当且仅当 End(G) 是一个 V 环时，End(G)/⊕End(Gp) 是一个 V 环。

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Abelian groups whose endomorphism rings are V-rings

We study Abelian groups whose endomorphism rings are V-rings. Let $G$ be a non-reduced Abelian group, We prove that $End (G)$ is a V-ring on either side if and only if $G = B \oplus ℚ^{n}$ where $B$ is a tame elementary Abelian group. We observe that a reduced group whose endomorphism is a V-ring, is an sp-group. Recognizing that $End (G)$ is also an sp-group of $\prod_{p \in ℙ} End (G_{p})$ , we show that $End (G) / \oplus End (G_{p})$ is a V-ring if and only if $End (G)$ is a V-ring.

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来源期刊

Journal of Algebra and Its Applications 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

226

审稿时长

4-8 weeks

期刊介绍： The Journal of Algebra and Its Applications will publish papers both on theoretical and on applied aspects of Algebra. There is special interest in papers that point out innovative links between areas of Algebra and fields of application. As the field of Algebra continues to experience tremendous growth and diversification, we intend to provide the mathematical community with a central source for information on both the theoretical and the applied aspects of the discipline. While the journal will be primarily devoted to the publication of original research, extraordinary expository articles that encourage communication between algebraists and experts on areas of application as well as those presenting the state of the art on a given algebraic sub-discipline will be considered.