交换环上的n-w-余纯投射模  

n-w-copure projective modules over commutative rings

作　　者：李庆 LI Qing(School of Mathematics,Southwest Minzu University,Chengdu 610041,China)

机构地区：[1]西南民族大学数学学院,四川成都610041

出　　处：《西南民族大学学报（自然科学版）》2021年第6期658-661,共4页Journal of Southwest Minzu University(Natural Science Edition)

基　　金：国家自然科学基金(11401493);西南民族大学中央高校基本科研业务费专项资金(2019NYB21)。

摘　　要：设R为具有单位元的交换环,引入了n-w-余纯投射R-模和(强)w-余纯投射R-模,讨论了n-w-余纯投射R-模和强w-余纯投射R-模在扩张之下的封闭性问题.证明了若R-模正合列0→A→B→C→0,其中A,C都是n-w-余纯投射模,则B也是n-w-余纯投射模.证明了若R-模正合列0→A→B→C→0,其中A,C都是强w-余纯投射模,则B也是强w-余纯投射模.给出了(n-)w-余纯投射R-模的等价刻画.证明了M是n-w-余纯投射R-模当且仅当对任意R-模正合列0→K→K'→M→0,其中K'是n-w-余纯投射R-模,则对任意N∈w-ζ_(n),诱导序列0→Hom_(R)(M,N)→Hom_(R)(K',N)→Hom_(R)(K,N)→0是w-正合列;当且仅当对任意R-模正合列0→A→B→C→0,其中A∈w-ζ_(n),则诱导序列0→Hom_(R)(M,A)→Hom_(R)(M,B)→Hom_(R)(M,C)→0是w-正合列.Let R be a commutative ring.n-w-copure projective R-modules and(strong)w-copure projective R-modules are introduced and studied.The closures under extensions of n-w-copure projective R-modules and strongly w-copure projective R-modules are considered respectively.It is proved that if an exact sequence of R-modules 0→A→B→C→0 with A and Cn-w-copure projective,then Bis also an n-w-copure projective R-module.It is shown that if an exact sequence of R-modules 0→A→B→C→0 with A and C strongly w-copure projective,then B is also strongly w-copure projective.The sufficiencies and necessities of (n-)w-copure projective R-modules are obtained.It is obtained that M is a n-w-copure projective R-module if and only if for any exact sequence of R-modules0→K→K'→M→0 with K′n-w-copure projective,the induced sequence 0→Hom_(R)(M,N)→Hom_(R)(K',N)→Hom_(R)(K,N)→0 is a w-exact sequence for anyN∈w-ζ_(n),and if and only if for any exact sequence of R-modules 0→A→B→C→0 with A∈w-ζ_(n),the induced sequence 0→Hom_(R)(M,A)→Hom_(R)(M,B)→Hom_(R)(M,C)→0 is a w-exact sequence.

关 键 词：n-余纯投射模 n-w-余纯投射模 强w-余纯投射模 w-正合列 

分 类 号：O153.3[理学—数学]