全素模和全半素模

IF 0.5 4区数学 Q3 MATHEMATICS

Bulletin of the Korean Mathematical Society Pub Date : 2020-01-01 DOI:10.4134/BKMS.B190864

J. Beachy, M. Medina-Bárcenas

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引用次数: 3

摘要

Blair和Tsutsui研究了全素数环(其中每个适当理想都是素数)，Courter研究了全半素数环(其中每个适当理想都是半素数)。对于给定模M，我们引入了全素数模和全半素数模的概念，并将Blair、Tsutsui、Courter的某些结果推广到M所生成的子范畴。我们还考虑了条件(1)M是一个全素数(半素数)模和(2)M的自同态环是一个全素数(半素数)环之间的关系。

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FULLY PRIME MODULES AND FULLY SEMIPRIME MODULES

Fully prime rings (in which every proper ideal is prime) have been studied by Blair and Tsutsui, and fully semiprime rings (in which every proper ideal is semiprime) have been studied by Courter. For a given module M , we introduce the notions of a fully prime module and a fully semiprime module, and extend certain results of Blair, Tsutsui, and Courter to the category subgenerated by M . We also consider the relationship between the conditions (1) M is a fully prime (semiprime) module, and (2) the endomorphism ring of M is a fully prime (semiprime) ring.

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来源期刊

Bulletin of the Korean Mathematical Society 数学-数学

CiteScore

0.80

自引率

20.00%

发文量

审稿时长

6 months

期刊介绍： This journal endeavors to publish significant research of broad interests in pure and applied mathematics. One volume is published each year, and each volume consists of six issues (January, March, May, July, September, November).