,On Regularity of Rings

来源 :代数集刊（英文版） | 被引量 : 0次 | 上传用户：yanwang114

【摘要】

：

It is shown that a ring R is (von Neumann) regular if and only if every cyclic left R-module is GP-injective, if and only if R is left PP and left GP-injective.

【作者】

：

Jianlong Chen Nanqing Ding

【机构】

：

Department of Applied Mathematics, Southeast University Nanjing 210096, China“,”Nanqing Ding Departm

【出处】

：

代数集刊（英文版）

【发表日期】

：

2001年3期

【关键词】

：

von Neumann regular ring P-injective module GP-injective module

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It is shown that a ring R is (von Neumann) regular if and only if every cyclic left R-module is GP-injective, if and only if R is left PP and left GP-injective. In addition, two examples are given to answer two open questions in the negative.

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