Y-Gorenstein内射复形
|
摘要
介绍并研究Y-Gorenstein内射复形,证明了复形C是Y-Gorenstein内射复形当且仅当每个层次上的模Cm是YGorenstein内射模.进而给出复形的Y-Gorenstein内射维数小于等于n的若干等价刻画.
Introduce and investigate Y-Gorenstein injective complexes,prove that the complex Cis YGorenstein injective complex if and only if every termCmis Y-Gorenstein injective module.Moreover,some characterizations of Y-Gorenstein injective dimensions of complexes less than or equal to nare given.
Introduce and investigate Y-Gorenstein injective complexes,prove that the complex Cis YGorenstein injective complex if and only if every termCmis Y-Gorenstein injective module.Moreover,some characterizations of Y-Gorenstein injective dimensions of complexes less than or equal to nare given.
引文
[1]Auslander M,Bridger M.Stable module theory[J].Memoirs of the American Mathematical Society,1969,94(94).
[2]Enochs E,Jenda O.Gorenstein injective and projective modules[J].Mathematische Zeitschrift,1995,220(1):611-633.
[3]Bravo D,Gillespie J.Absolutely Clean,Level,and Gorenstein AC-Injective Complexes[J].Communications in Algebra,2014,44(5):2213-2233.
[4]Enochs E E,Jenda O M G.Relative Homological Algebra[M].Berlin:Walter de Gruyter,2000:67-114.
[5]Enochs E,Jenda O G,J.A.López-ramos.Covers and Envelopes by V-Gorenstein Modules[J].Communications in Algebra,2005,33(12):4705-4717
[6]Geng Y,Ding N.W-Gorenstein modules.[J].Journal of Algebra,2011:132-146.
[7]Huang Z.Proper resolutions and Gorenstein categories[J].Journal of Algebra,2013,393(11):142-169.
[8]Meng F,Pan Q.X-Gorenstein Projective and Y-Gorenstein Injective Modules[J].Hacettepe University Bulletin of Natural Sciences&Engineering,2011,40(4):537-554.
[9]Enochs E,Rozas J.Gorenstein injective and projective complexes[J].Communications in Algebra,1998,26(5):1657-1674.
[10]García Rozas J R.Covers and envelopes in the category of complexes of modules[M].Chapman&Hall/CRC Press,1999.
[11]Liu Z,Zhang C.Gorenstein injective complexes of modules over Noetherian rings☆[J].Journal of Algebra,2009,321(5):1546-1554.
[12]杨刚.Gorenstein投射、内射和平坦复形.数学学报中文版[J],2011,54(3):451-459.
[13]Zhao R Y,Ren W.VW-Gorenstein complexes[J].Turkish Journal of Mathematics 2017,41:537-547.
[14]Bashir R E.Covers and Directed Colimits[J].Algebras&Representation Theory,2006,9(5):423-430.
[2]Enochs E,Jenda O.Gorenstein injective and projective modules[J].Mathematische Zeitschrift,1995,220(1):611-633.
[3]Bravo D,Gillespie J.Absolutely Clean,Level,and Gorenstein AC-Injective Complexes[J].Communications in Algebra,2014,44(5):2213-2233.
[4]Enochs E E,Jenda O M G.Relative Homological Algebra[M].Berlin:Walter de Gruyter,2000:67-114.
[5]Enochs E,Jenda O G,J.A.López-ramos.Covers and Envelopes by V-Gorenstein Modules[J].Communications in Algebra,2005,33(12):4705-4717
[6]Geng Y,Ding N.W-Gorenstein modules.[J].Journal of Algebra,2011:132-146.
[7]Huang Z.Proper resolutions and Gorenstein categories[J].Journal of Algebra,2013,393(11):142-169.
[8]Meng F,Pan Q.X-Gorenstein Projective and Y-Gorenstein Injective Modules[J].Hacettepe University Bulletin of Natural Sciences&Engineering,2011,40(4):537-554.
[9]Enochs E,Rozas J.Gorenstein injective and projective complexes[J].Communications in Algebra,1998,26(5):1657-1674.
[10]García Rozas J R.Covers and envelopes in the category of complexes of modules[M].Chapman&Hall/CRC Press,1999.
[11]Liu Z,Zhang C.Gorenstein injective complexes of modules over Noetherian rings☆[J].Journal of Algebra,2009,321(5):1546-1554.
[12]杨刚.Gorenstein投射、内射和平坦复形.数学学报中文版[J],2011,54(3):451-459.
[13]Zhao R Y,Ren W.VW-Gorenstein complexes[J].Turkish Journal of Mathematics 2017,41:537-547.
[14]Bashir R E.Covers and Directed Colimits[J].Algebras&Representation Theory,2006,9(5):423-430.