| Title:
|
Copure injective resolutions, flat resolvents and dimensions (English) |
| Author:
|
Enochs, Edgar E. |
| Author:
|
Overtoun, Jenda M. G. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
34 |
| Issue:
|
2 |
| Year:
|
1993 |
| Pages:
|
203-211 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
preenvelopes |
| Keyword:
|
copure injective |
| Keyword:
|
copure flat |
| Keyword:
|
$n$-Gorenstein |
| Keyword:
|
resolutions |
| MSC:
|
13H10 |
| MSC:
|
16D50 |
| MSC:
|
16E30 |
| MSC:
|
18G05 |
| MSC:
|
18G10 |
| MSC:
|
18G15 |
| idZBL:
|
Zbl 0780.18006 |
| idMR:
|
MR1241728 |
| . |
| Date available:
|
2009-01-08T18:02:33Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118572 |
| . |
| Reference:
|
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| Reference:
|
[2] Bernecker H.: Flatness and absolute purity applying functor categories to ring theory.J. Algebra 44 (1977), 411-419. Zbl 0352.18020, MR 0432707 |
| Reference:
|
[3] Enochs E.: Injective and flat covers, envelopes and resolvents.Israel J. Math. 39 (1981), 189-209. Zbl 0464.16019, MR 0636889 |
| Reference:
|
[4] Enochs E., Jenda O.: Balanced functors applied to modules.J. Algebra 92 (1985), 303-310. Zbl 0554.18006, MR 0778450 |
| Reference:
|
[5] Enochs E., Jenda O.: Resolvents and dimensions of modules and rings.Arch. Math. 56 (1991), 528-532. Zbl 0694.16012, MR 1106493 |
| Reference:
|
[6] Enochs E., Jenda O.: Copure injective modules.Quaest. Mathematicae 14 (1991), 401-409. Zbl 0747.16003, MR 1143044 |
| Reference:
|
[7] Gabriel P.: Objects injectifs dans les catégories abéliennes.Sém. Dubreil, 1958/59, 17/01-17/32, Paris, 1960. Zbl 0214.03301 |
| Reference:
|
[8] Iwanaga Y.: On rings with finite self-injective dimension II.Tsukuba J. Math. 4 (1980), 107-113. Zbl 0459.16011, MR 0597688 |
| Reference:
|
[9] Jenda O.: The dual of the grade of a module.Arch. Math. 51 (1988), 297-302. Zbl 0632.16018, MR 0964954 |
| Reference:
|
[10] 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 |
| Reference:
|
[11] Lenzing H.: Endlich präsentierbare modulen.Arch. Math. 20 (1969), 262-266. MR 0244322 |
| . |
