[1] Song Xianmei, Chen Jianlong,. Notes on pure projective modules [J]. Journal of Southeast University (English Edition), 2005, 21 (4): 506-508. [doi:10.3969/j.issn.1003-7985.2005.04.026]
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Notes on pure projective modules(
)
)Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]
- Volumn:
- 21
- Issue:
- 2005 4
- Page:
- 506-508
- Research Field:
- Mathematics, Physics, Mechanics
- Publishing date:
- 2005-12-30
Info
- Title:
- Notes on pure projective modules
- Author(s):
- Song Xianmei1; 2; Chen Jianlong1
-
1Department of Mathematics, Southeast University, Nanjing 210096, China
2Department of Mathematics, Anhui Normal University, Wuhu 241000, China
- Keywords:
- pure projective left R-module; pure injective left R-module; pure submodule; pure exact sequence
- PACS:
- O153.3
- DOI:
- 10.3969/j.issn.1003-7985.2005.04.026
- Abstract:
- Let R be an associated ring with identity.A new equivalent characterization of pure projective left R-modules is given by applying homological methods.It is proved that a left R-module P is pure projective if and only if for any pure epimorphism E →M →0, where E is pure injective, HomR(P, E)→HomR(P, M)→0 is exact.Also, we obtain a dual result of pure injective left R-modules.Furthermore, it is shown that every pure projective left R-module is closed under pure submodule if and only if every pure injective left R-module is closed under pure epimorphic image.
References:
[1] Azumaga G. Locally pure projective modules[J].Contemporary Mathematics, 1992, 124:17-22.
[2] Enochs E E, Jenda O M G.Relative homological algebra[M].Berlin:Walter de Gruyter, 2000.110-119.
[3] Wisbaue R.Foundations of module and ring theory[M].Philadelphia:Gordon and Breach Science, 1991.281-296.
[4] Jr Warfield R B.Purity and algebraic compactness for modules[J].Pacific J Math, 1969, 28(3):699-719.
[5] Xu J Z.Flat covers of modules[M].Berlin:Springer-Verlag, 1996.38-80.
Memo
- Memo:
- Biographies: Song Xianmei(1977—), female, lecturer, graduate;Chen Jianlong(corresponding author), male, professor, jlchen@seu.edu.cn.
Last Update: 2005-12-20