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Restricted Projective,Injective And Flat Complexes

Posted on:2020-04-08Degree:MasterType:Thesis
Country:ChinaCandidate:Y H SongFull Text:PDF
GTID:2370330578956696Subject:Basic mathematics
Abstract/Summary:PDF Full Text Request
Over an associative ring R,firstly,the notions of restricted injective modules are in-troduced by derived functors.We show that Gorenstein injective modules are restricted injective modules,but not vice versa.The classical restricted injective dimension is inves-tigated using resolutions by restricted injective modules,and some new methods are given to compute the restricted injective dimension.The relationship between restricted injec-tive modules and strongly torsion-free modules are investigated.Secondly,the notions of restricted projective,restricted injective and restricted flat complexes are introduced,and some characterizations and properties are given.It is shown in the paper that a complex C is restricted projective if and only if Cm is a restricted projective module for each m?Z,and each morphism from C to L is homotopic to 0 whenever L is a complex of finite injective dimension.If furthermore C is bounded right,then C is restricted projective if and only if Cm is a restricted projective module for each m?Z.In addition,if C is an exact complex of R-modules,then C is restricted projective if and only if Zm(C)is a restricted projective module for each m ? Z.Similarly,restricted injective and restricted flat versions of all these results are given.
Keywords/Search Tags:restricted injective module, restricted injective dimension, restricted projective complex, restricted injective complex, restricted flat complex, cover, en-velope
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