(m,n)-投射模与(m,n)-遗传环

详细信息    查看全文 | 推荐本文 |

英文篇名：(m,n)-Projective Modules and(m,n)-Hereditary Rings 作者：杨璐璐 ; 赵仁育 英文作者：YANG Lulu;ZHAO Renyu;College of Mathematics and Statistics,Northwest Normal University; 关键词：(m ; n)-投射模 ; (m ; n)-内射模 ; (m ; n)-遗传环 英文关键词：(m,n)-projective module;;(m,n)-injective module;;(m,n)-hereditary ring 中文刊名：JLDX 英文刊名：Journal of Jilin University(Science Edition) 机构：西北师范大学数学与统计学院; 出版日期：2019-03-26 出版单位：吉林大学学报(理学版) 年：2019 期：v.57;No.236 基金：国家自然科学基金(批准号:11861055) 语种：中文; 页：JLDX201902009 页数：5 CN：02 ISSN：22-1340/O 分类号：59-63

摘要

设m,n是两个任意取定的正整数,通过引入(m,n)-遗传环的概念,利用函子的正合性方法,给出(m,n)-投射模和(m,n)-遗传环的一些等价刻画.
        Let m,n be two arbitrary positive integers.By introducing the concept of(m,n)-hereditary rings,and using the exact method of functor,we gave some characterizations of(m,n)-projective modules and(m,n)-hereditary rings.

引文

[1]MAO Lixin,DING Nanqing.FP-Projective Dimensions[J].Communications in Algebra,2005,33(4):1153-1170.
    [2]MORADZADEH-DEHKORDI A,SHOJAEE S H.Rings in Which Every Ideal Is Pure-Projective or FP-Projective[J].Journal of Algebra,2017,478:419-436.
    [3]GENG Yuxian.f-Projective and f-Injective Modules[J].Journal of Mathematical Research&Exposition,2008,28(1):74-80.
    [4]CHEN Jianlong,DING Nanqing,LI Yuanlin,et al.On(m,n)-Injectivity of Modules[J].Communications in Algebra,2001,29(12):5589-5603.
    [5]MAO Lixin,DING Nanqing.On Relative Injective Modules and Relative Coherent Rings[J].Communications in Algebra,2006,34(7):2531-2545.
    [6]ZHANG Xiaoxiang,CHEN Jianlong,ZHANG Juan.On(m,n)-Injective Modules and(m,n)-Coherent Rings[J].Algebra Colloquium,2005,12(1):149-160.
    [7]SHAMSUDDIN A.n-Injective and n-Flat Modules[J].Communications in Algebra,2001,29(5):2039-2050.
    [8]GUPTA R N.On f-Injective Modules and Semi-hereditary Rings[J].Proceedings of the National Institute of Sciences of India,Part A:Physical Sciences,1969,35:323-328.
    [9]ZHU Zhanmin,CHEN Jianlong,ZHANG Xiaoxiang.On(m,n)-Purity of Modules[J].East-West Journal of Mathematics,2003,5(1):35-44.