论文信息 - Covers and Envelopes in Grothendieck Categories: Flat Covers of Complexes with Applications

Covers and Envelopes in Grothendieck Categories: Flat Covers of Complexes with Applications

Abstract In the general setting of Grothendieck categories with enough projectives, we prove theorems that make possible to restrict the study of the problem of the existence of F -covers and envelopes to the study of some properties of the class F . We then prove the existence of flat covers and cotorsion envelopes of complexes, giving some examples. This generalizes the earlier work (J. Algebra201 (1998), 86–102) and finishes the problem of the existence of flat covers of complexes.

E. Enochs | L. Oyonarte | J. R. G. Rozas | S. Aldrich

[1] E. Enochs,et al. All Modules Have Flat Covers , 2001 .

[2] P. Eklof,et al. How To Make Ext Vanish , 2001 .

[3] G. Rozas,et al. Covers and envelopes in the category of complexes of modules , 1999 .

[4] E. Enochs,et al. Flat Covers of Complexes , 1998 .

[5] Jinzhong Xu. Flat covers of modules , 1996 .

[6] Overtoun M. G. Jenda,et al. Orthogonality in the Category of Complexes , 1996 .

[7] L. L. Avramov,et al. Homological dimensions of unbounded complexes , 1991 .

[8] N. Spaltenstein. Resolutions of unbounded complexes , 1988 .

[9] E. Enochs. Injective and flat covers, envelopes and resolvents , 1981 .

[10] L. Salce. Cotorsion theories for abelian groups , 1979 .

[11] B. Osofsky. Projective dimension of “nice” directed unions , 1978 .

[12] P. Eklof. Homological algebra and set theory , 1977 .

[13] D. Rees. ELÉMENTS DE GÉOMÉTRIE ALGÉBRIQUE–I , 1972 .

[14] H. Bass. Finitistic dimension and a homological generalization of semi-primary rings , 1960 .