用纯注入性描述拟frobenius环

IF 0.6 4区数学 Q3 MATHEMATICS

Bulletin of the Korean Mathematical Society Pub Date : 2020-01-01 DOI:10.4134/BKMS.B190247

A. MORADZADEH-DEHKORDI

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引用次数: 0

摘要

如果环R对纯精确序列是单射的，则称其为右纯单射。根据L. Melkersson的一个众所周知的结果，每个可交换的Artinian环都是纯内射的，但即使R是一个可交换的noether局部环，其逆也不成立。本文给出了右纯注入环是右Artinian环或拟frobenius环的一系列条件。此外，我们的一些结果扩展了先前已知的准frobenius环的结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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SOME NEW CHARACTERIZATIONS OF QUASI-FROBENIUS RINGS BY USING PURE-INJECTIVITY

A ring R is called right pure-injective if it is injective with respect to pure exact sequences. According to a well known result of L. Melkersson, every commutative Artinian ring is pure-injective, but the converse is not true, even if R is a commutative Noetherian local ring. In this paper, a series of conditions under which right pure-injective rings are either right Artinian rings or quasi-Frobenius rings are given. Also, some of our results extend previously known results for quasi-Frobenius rings.

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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).