PDF(402 KB)
The Existence of #-injective Envelopes of Complexes
Li LIANG, Gang YANG
Acta Mathematica Sinica, Chinese Series ›› 2019, Vol. 62 ›› Issue (3) : 391-396.
PDF(402 KB)
PDF(402 KB)
The Existence of #-injective Envelopes of Complexes
Let dwI denote the class of #-injective complexes of left R-modules (i.e., complexes of injective left R-modules). We prove that over left noetherian rings R, the pair (⊥(dwI), dwI) is a perfect injective cotorsion pair. In particular, we get that every complex of left R-modules has a #-injective envelope. As an application, we prove that over left noetherian rings R, every complex of left R-modules has a special Etac (I)-preenvelope, where Etac (I) is the class of complete acyclic complexes of injective left R-modules.
#-injective complex / cover / envelope / cotorsion pair {{custom_keyword}} /
[1] Enochs E. E., Injective and flat covers, envelopes and resolvents, Israel J. Math., 1981, 39:189-209.
[2] Enochs E. E., Jenda O. M. G., Relative Homological Algebra, Walter de Gruyter, Berlin-New York, 2000.
[3] Enochs E. E., Jenda O. M. G., López-Ramos J. A., The existence of Gorenstein flat covers, Math. Scand., 2004, 94:46-62.
[4] Enochs E. E., Jenda O. M. G., Xu J., Orthogonality in the category of complexes, Math. J. Okayama Univ., 1996, 38:25-46.
[5] García Rozas J. R., Covers and Envelopes in the Category of Complexes of Modules, CRC Press, Boca Raton-London-New York-Washington, D.C., 1999.
[6] Gillespie J., Gorenstein complexes and recollements from cotorsion pairs, Adv. Math., 2016, 291:859-911.
[7] Iacob A., DG-injective covers, #-injective covers, Comm. Algebra, 2011, 39:1673-1685.
[8] Liang L., Ding N., On #-injective complexes, J. Algebra Appl., 2012, 11:1250021(22 pages).
[9] Liang L., Ding N., Yang G., Covers and envelopes by #-F complexes, Comm. Algebra, 2011, 39:3253-3277.
[10] Yang G., Liu Z., Cotorsion pairs and model structures on Ch(R), Proc. Edinb. Math. Soc., 2011, 54:783-797.
PDF(402 KB)
/
| 〈 |
|
〉 |
