交换超环上的矩阵
Matrices over Commutative Hyperrings
DOI: 10.12677/PM.2020.1012134, PDF,    科研立项经费支持
作者: 黄冬明, 王 鑫：海南大学理学院，海南 海口
关键词: Krasner超环；Salvo超环；超理想；Krasner Hyperrings； Salvo Hyperrings； Hyperideals
摘要: 本文旨在研究Krasner交换超环R与其上的全矩阵环Mnxn(R)之间的一些内在联系，建立了一个从R的超理想集合到Mnxn(R)的超理想集合之间的双射。进一步，又得到了结论：R是单(素)超环当且仅当Mnxn(R)是单(素)超环。
Abstract: The main aim of this paper is to study the interplay between a commutative Krasner hyperring R and the matrix ring Mnxn(R) over it. A bijection from the hyperideals set of R to the hyperideals set of Mnxn(R) is established. Furthermore, it is concluded that R is a simple (res. prime) hyperring if and only if Mnxn(R) is a simple (res. prime) hyperring.
文章引用：黄冬明, 王鑫. 交换超环上的矩阵[J]. 理论数学, 2020, 10(12): 1131-1137. https://doi.org/10.12677/PM.2020.1012134

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