LIU Yunping,JIN Hailan.The regular rings with strongly injective[J].Journal of Yanbian University,2022,(01):37-40.
一类具强内射的正则环
- Title:
- The regular rings with strongly injective
- 文章编号:
- 1004-4353(2022)01-0037-04
- 分类号:
- O153.3
- 文献标志码:
- A
- 摘要:
- 研究了正则环与强CP - 内射环的等价关系,证明了当R为MELT环时, R的正则性与弱正则性是等价的,同时证明了当R为约化环时, R的正则性与强CP - 内射性的等价关系,并得出了当R为半本原左拟 - duo环时, R的正则性、弱正则性与强CP - 内射性是等价的.
- Abstract:
- We studied the equivalence relationship between regular rings and strong completely principal injective rings.It is proved that the regularity of R is equivalent to weak regularity when R is MELT ring, and the regularity of R is equivalent to strong CP - injective when R is reduced ring.And it is concluded that when R is semiprimitive left quasi - duo ring, the regularity and weak regularity of R are equivalent to the strong CP - injective property.
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备注/Memo
收稿日期: 2021-10-17
第一作者: 刘云萍(1997—),女,硕士研究生,研究方向为代数学(环论).
通信作者: 金海兰(1963—),女,理学博士,教授,研究方向为代数学(环论).