关于GI-平坦模的注记
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摘要
利用GI-平坦模与Gorenstein平坦维数给出了平坦模的另一等价刻划,并得到了环R是左Gorenstein半遗传环时,右R模M是GI-平坦模当且仅当M是平坦模;在交换环的条件下利用Hom函子,A函子刻划了GI-平坦模;另外还给出了短正合列上的模的GI平坦维数的关系.
By using the concept of GI-flat module and Gorenstein flat dimension,a new characterization of flat modules is put forward.It is also proved that: if R is left Gorenstein semihereditary,M is GI-flat if and only if M is flat;if R is commutative,by using Hom functor and functor,some equivalence characterizations of GI-flat modules are given;let 0→A→B→C→0 be an exact sequence of right R-modules,the relationship between these modules ' GI-flat dimension is discussed.
By using the concept of GI-flat module and Gorenstein flat dimension,a new characterization of flat modules is put forward.It is also proved that: if R is left Gorenstein semihereditary,M is GI-flat if and only if M is flat;if R is commutative,by using Hom functor and functor,some equivalence characterizations of GI-flat modules are given;let 0→A→B→C→0 be an exact sequence of right R-modules,the relationship between these modules ' GI-flat dimension is discussed.
引文
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[4]Enochs E E,Jenda O M G.Relative Homological algebra[M].Berlin:Walter de Gruyter,2000.
[5]Anderson F W,Fuller K R.Rings and categories of modules[M].New York:Springer-Verlag,1974.
[6]Zhao G Q,Huang Z Y.n-strongly gorenstein projective,injective and flat modules[J].Comm in Alg,2011,39(8):3 044-3 062.
[7]Mahdou N,Tamekkante M.on(Strongly)Gorenstein(Semi)Hereditary rings[J].Arab J Sci Eng,2011,36(3):431-440.
[8]Ware R.Endomorphism rings of projective modules[J].Trans Amer Math Soc,1971,155:233-259.
[2]Gao Z H.On GI-injective modules[J].Comm Algebra,2012,40(10):3 841-3 858.
[3]Gao Z H.On GI-flat modules and dimensions[J].Korean Math Soc,2013,50(1):203-218.
[4]Enochs E E,Jenda O M G.Relative Homological algebra[M].Berlin:Walter de Gruyter,2000.
[5]Anderson F W,Fuller K R.Rings and categories of modules[M].New York:Springer-Verlag,1974.
[6]Zhao G Q,Huang Z Y.n-strongly gorenstein projective,injective and flat modules[J].Comm in Alg,2011,39(8):3 044-3 062.
[7]Mahdou N,Tamekkante M.on(Strongly)Gorenstein(Semi)Hereditary rings[J].Arab J Sci Eng,2011,36(3):431-440.
[8]Ware R.Endomorphism rings of projective modules[J].Trans Amer Math Soc,1971,155:233-259.