兰州理工大学学报

兰州理工大学学报 ›› 2021, Vol. 47 ›› Issue (4): 149-156.

• 数理科学 • 上一篇    下一篇

X-丁投射模

吴德军*, 宋梦钰   

  1. 兰州理工大学 理学院, 甘肃 兰州 730050
  • 收稿日期:2020-01-02 出版日期:2021-08-01 发布日期:2021-09-07
  • 通讯作者: 吴德军(1978-),男,甘肃金昌人,博士,教授.Email:wudj@lut.edu.cn
  • 基金资助:
    国家自然科学基金(11761047)

X-Ding projective modules

WU De-jun, SONG Meng-yu   

  1. School of Science, Lanzhou Univ. of Tech., Lanzhou 730050, China
  • Received:2020-01-02 Online:2021-08-01 Published:2021-09-07

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摘要： 设R是具有单位元的结合环, X是包含所有平坦模的R-模类.引入X-丁投射模和X-丁投射维数的定义并研究了相关性质.如果存在正合列P=∶…→P1→P0→P0→P1→…, 其中Pi, Pi是投射模, i∈Z, 对于任意R-模F∈X,HomR(－, F)作用在正合列P上保持正合,并且M=Ker(P0→P1), 那么称M是X-丁投射模. 证明了X-丁投射模类是投射可解的并且X-丁投射模保持直和与直和项,同时证明了若GX-Dpd(R)<∞,则(X-DP(R),(X-DP(R))⊥)是完备遗传余挠对.

关键词: X-丁投射模, X-丁投射维数, 余挠对

Abstract: Let R be an associative ring with identity and X is a class that contains all flat R-modules, the definitions of X-Ding projective modules and X-Ding projective dimensions are introduced and the relative properties are studied. A right R-module M is called X-Ding projective if there exists an exact sequenceP=∶…→P1→P0→P0→P1→…of projective right R-modules such that M=Ker (P0→P1) andHomR(P,F) is exact whenever F∈X. It is proved that the class of all X-Ding projective modules is projectively resolving and is closed under direct sums and direct summands. In addition, it is proved that ifGX-Dpd(R)<∞,then (X-DP(R), (X-DP(R))⊥) is a complete here ditary cotorsion pair.

Key words: X-Ding projective module, X-Ding projective dimension, cotorsionpair

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