Copure injective resolutions, flat resolvents and dimensions
Enochs, Edgar E. ; Overtoun, Jenda M. G.
Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993), p. 203-211 / Harvested from Czech Digital Mathematics Library
Access to full text
Full (PDF)

In this paper, we show the existence of copure injective preenvelopes over noetherian rings and copure flat preenvelopes over commutative artinian rings. We use this to characterize $n$-Gorenstein rings. As a consequence, if the full subcategory of strongly copure injective (respectively flat) modules over a left and right noetherian ring $R$ has cokernels (respectively kernels), then $R$ is $2$-Gorenstein.

Publié le : 1993-01-01
Classification:  13H10,  16D50,  16E30,  18G05,  18G10,  18G15 
@article{118572,
     author = {Edgar E. Enochs and Jenda M. G. Overtoun},
     title = {Copure injective resolutions, flat resolvents and dimensions},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {34},
     year = {1993},
     pages = {203-211},
     zbl = {0780.18006},
     mrnumber = {1241728},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118572}
}

Enochs, Edgar E.; Overtoun, Jenda M. G. Copure injective resolutions, flat resolvents and dimensions. Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) pp. 203-211. http://gdmltest.u-ga.fr/item/118572/

Auslander M.; Bridger M. Stable module theory, Memories of the Amer. Math. Soc. 94 (1969), 1-146. (1969) | MR 0269685 | Zbl 0204.36402

Bernecker H. Flatness and absolute purity applying functor categories to ring theory, J. Algebra 44 (1977), 411-419. (1977) | MR 0432707 | Zbl 0352.18020

Enochs E. Injective and flat covers, envelopes and resolvents, Israel J. Math. 39 (1981), 189-209. (1981) | MR 0636889 | Zbl 0464.16019

Enochs E.; Jenda O. Balanced functors applied to modules, J. Algebra 92 (1985), 303-310. (1985) | MR 0778450 | Zbl 0554.18006

Enochs E.; Jenda O. Resolvents and dimensions of modules and rings, Arch. Math. 56 (1991), 528-532. (1991) | MR 1106493 | Zbl 0694.16012

Enochs E.; Jenda O. Copure injective modules, Quaest. Mathematicae 14 (1991), 401-409. (1991) | MR 1143044 | Zbl 0747.16003

Gabriel P. Objects injectifs dans les catégories abéliennes, Sém. Dubreil, 1958/59, 17/01-17/32, Paris, 1960. | Zbl 0214.03301

Iwanaga Y. On rings with finite self-injective dimension II, Tsukuba J. Math. 4 (1980), 107-113. (1980) | MR 0597688 | Zbl 0459.16011

Jenda O. The dual of the grade of a module, Arch. Math. 51 (1988), 297-302. (1988) | MR 0964954 | Zbl 0632.16018

Jensen C. Les foncteurs derives de $øverset {\lim}\to {\longleftarrow}$ et leurs applications en theorie des modules, Lecture Notes in Mathematics 254, Springer, 1972. | MR 0407091

Lenzing H. Endlich präsentierbare modulen, Arch. Math. 20 (1969), 262-266. (1969) | MR 0244322