[1]赵 伟,张晓磊.非诣零内射模[J].四川师范大学学报(自然科学版),2019,(06):808-815.[doi:10.3969/j.issn.1001-8395.2019.06.016]
 ZHAO Wei,ZHANG Xiaolei.On Nonnil-injective Modules[J].Journal of SichuanNormal University,2019,(06):808-815.[doi:10.3969/j.issn.1001-8395.2019.06.016]
点击复制

非诣零内射模()
分享到:

《四川师范大学学报(自然科学版)》[ISSN:1001-8395/CN:51-1295/N]

卷:
期数:
2019年06期
页码:
808-815
栏目:
基础理论
出版日期:
2019-11-04

文章信息/Info

Title:
On Nonnil-injective Modules
文章编号:
1001-8395(2019)06-0808-08
作者:
赵 伟1 张晓磊2
1.阿坝师范学院 数学与计算机学院, 四川 汶川 623002; 2.成都航空职业技术学院 基础教学部, 四川 成都 610100
Author(s):
ZHAO Wei1 ZHANG Xiaolei2
1.School of Mathematics and Computer Science, Aba Teachers University, Wenchuan 623002, Sichuan; 2.Basic Teaching Department, Chengdu Aeronautic Polytechnic, Chengdu 610100, Sichuan
关键词:
φ-挠模 非诣零内射模 非诣零内射包
Keywords:
φ-torsion modules nonnil-injective modules nonnil-injective hull
分类号:
O153.3
DOI:
10.3969/j.issn.1001-8395.2019.06.016
文献标志码:
A
摘要:
一个交换环的诣零根若为可除的素理想,则这个交换环称为φ-环.介绍φ-环上的φ-挠模,调查φ-环上的非诣零内射模与非诣零内射包,同时刻画非诣零半单环.
Abstract:
A commutative ring with a divided prime nil radical is called a φ-ring.In this paper, we introduce φ-torsion modules over a φ-ring, investigate nonnil-injective modules the nonnil-injective hull over a φ-ring and characterize the nonnil-semisimple rings.

参考文献/References:

[1] HEDSTROM J R, HOUSTON E G.Pseudo-valuation domains[J].Pacific J Math,1978,75(1):137-147.
[2] BADAWI A, ANDERSON D F, DOBBS D E.Pseudo-valuation Rings[M].Basel:Marcel Dekker,1997:57-67.
[3] BADAWI A.On φ-pseudo-valuation Rings[M].Basel:Marcel Dekker,1999.
[4] BADAWI A.On Nonnil-Noetherian rings[J].Comm Algebra,2003,31(4):1669-1677.
[5] BADAWI A.On φ-pseudo-valuation rings II[J].Houston J Math,2000,26(3):473-480.
[6] BADAWI A.On φ-chained rings and φ-pseudo-valuation rings[J].Houston J Math,2001,27(4):725-736.
[7] BADAWI A.On divided rings and φ-pseudo-valuation rings[J].International J Comm Rings,2002,1(2):51-60.
[8] ANDERSON D F, BADAWI A.On φ-Prüfer rings and φ-Bezout rings[J].Houston J Math,2004,30(2):331-343.
[9] ANDERSON D F, BADAWI A.on φ-Dedekind rings and φ-Krull rings[J].Houston J Math,2005,31(4):1007-1022.
[10] BADAWI A, LUCAS T.‘Rings with Prime Nilradical' Arithmetical Properties of Commutative Rings and Monoids[M].Chapman Hall:CRC,2005:198-212.
[11] BADAWI A.Factoring nonnil ideals as a product of prime and invertible ideals[J].Bulletin of the London Math Society,2005,37(1):665-672.
[12] BADAWI A, LUCAS T.On φ-Mori rings[J].Houston J Math,2006,32(1):1-32.
[13] KIM H, WANG F G.On φ-strong Mori rings[J].Houston J Math,2012,38(2):359-371.
[14] HIZEM S, BENHIGGI A.On nonnil-Noetherian rings and the SFT property[J].Rocky Mountain J Math,2011,41(5):1483-1500.
[15] BACEM K, ALI B.Nonnil-coherent rings[J].Beitr Algebra Geom,2016,57(2):297-305.
[16] 杨晓燕.环和模的广义 Noetherian 性[D].兰州:西北师范大学,2006.
[17] ZHAO W, WANG F G, TANG G H.On Phi-von Neumann regularrings[J].J Korean Math Soc,2012,50(1):219-229.
[18] CRIVEI S.Injective Modules Relative to Torsion Theories[M].Romania:Cluj-Napoca,2004:4-14.

备注/Memo

备注/Memo:
收稿日期:2018-03-23 接受日期:2019-04-10 基金项目:国家自然科学基金(11861001)、四川省应用基础研究(2018JY0458)、四川省高校科研创新团队建设计划(18TD0047)和四川省教育厅项目(18ZB0012) 第一作者简介:赵 伟(1982—),男,博士,主要从事环与同调和代数K-理论的研究,E-mail:zw9c248@163.com
更新日期/Last Update: 2019-11-04