[1] Zhang Xiaoxiang, Chen Jianlong,. Homological properties of modules characterized by matrices [J]. Journal of Southeast University (English Edition), 2005, 21 (2): 239-243. [doi:10.3969/j.issn.1003-7985.2005.02.025]
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Homological properties of modules characterized by matrices(
)
)Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]
- Volumn:
- 21
- Issue:
- 2005 2
- Page:
- 239-243
- Research Field:
- Mathematics, Physics, Mechanics
- Publishing date:
- 2005-06-30
Info
- Title:
- Homological properties of modules characterized by matrices
- Author(s):
- Zhang Xiaoxiang; Chen Jianlong
- Department of Mathematics, Southeast University, Nanjing 210096, China
- Keywords:
- (α; β)-injective module; (α; β)-flat module; R-ML module; (α; β)-coherent ring
- PACS:
- O154
- DOI:
- 10.3969/j.issn.1003-7985.2005.02.025
- Abstract:
- Some homological properties of R-modules were investigated by matrices over a ring R.Given two cardinal numbers α, β and an α×β row-finite matrix A, it was proved that Ext1R R (R(α)/R(β)A()(), M)=0 if and only if Mα/rMα(R(β)A())≅ HomRR(R(β)A(), M)if and only if rMβMlR(β)()(A)=AMα.Thus, the notion of(m, n)-injectivity was extended.Moreover, (α, β)-flatness was characterized via annihilators of matrices, factorizations of homomorphisms as well as homological groups so that(m, n)-flat modules, f-projective modules and n-projective modules were consolidated under the notion of(α, β)-flat modules.Furthermore, a characterization of left R-ML modules and some equivalent conditions for R(β)A ()to be left R-ML were presented.Consequently, the notions of coherent rings, (m, n)-coherent rings and π-coherent rings were consolidated under that of(α, β)-coherent rings.
References:
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Memo
- Memo:
- Biographies: Zhang Xiaoxiang(1977—), male, graduate;Chen Jianlong(corresponding author), male, doctor, professor, jlchen@seu.edu.cn.