| Title:
|
On some classes of modules (English) |
| Author:
|
Güngöroglu, Gonca |
| Author:
|
Harmanci, Abdullah |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
50 |
| Issue:
|
4 |
| Year:
|
2000 |
| Pages:
|
839-846 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The aim of this paper is to investigate quasi-corational, comonoform, copolyform and $\alpha $-(co)atomic modules. It is proved that for an ordinal $\alpha $ a right $R$-module $M$ is $\alpha $-atomic if and only if it is $\alpha $-coatomic. And it is also shown that an $\alpha $-atomic module $M$ is quasi-projective if and only if $M$ is quasi-corationally complete. Some other results are developed. (English) |
| Keyword:
|
quasi-corational module |
| Keyword:
|
copolyform module |
| Keyword:
|
$\alpha $-coatomic module |
| MSC:
|
16D10 |
| MSC:
|
16D80 |
| MSC:
|
16D99 |
| idZBL:
|
Zbl 1079.16501 |
| idMR:
|
MR1792973 |
| . |
| Date available:
|
2009-09-24T10:38:17Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127613 |
| . |
| Reference:
|
[1] T. Albu and P. F. Smith: Dual relative Krull dimension of modules over commutative rings. Abelian groups.Math. Appl. (East European Ser.) 343 (1995), 1–15. MR 1378184 |
| Reference:
|
[2] F. W. Anderson and K. R. Fuller: Rings and Categories.Springer-Verlag, New York, 1973. |
| Reference:
|
[3] R. Courter: Finite direct sums of complete matrix rings over perfect completely primary rings.Canad. J. Math. 21 (1968), 430–446. MR 0257141, 10.4153/CJM-1969-047-0 |
| Reference:
|
[4] F. Kasch: Modules and Rings.Academic Press, 1982. Zbl 0523.16001, MR 0667346 |
| Reference:
|
[5] D. Kirby: Dimension and length for artinian modules.Quart. J. Math. Oxford Ser. 2 41 (1990), 419–429. Zbl 0724.13015, MR 1081104, 10.1093/qmath/41.4.419 |
| Reference:
|
[6] S. H. Mohammed and B. J. Muller: Continuous and Discrete Modules.London Math. Soc. Lecture Notes 147, Cambridge Univ. Press, 1990. MR 1084376 |
| Reference:
|
[7] K. Oshiro: Semiperfect modules and quasi-semiperfect modules.Osaka J. Math. 20 (1983), 337–372. Zbl 0516.16015, MR 0706241 |
| Reference:
|
[8] R. N. Roberts: Krull dimension for Artinian modules over quasi-local commutative Rings.Quart. J. Math. Oxford Ser. 3 26 (1975), 269–273. Zbl 0311.13006, MR 0389884, 10.1093/qmath/26.1.269 |
| Reference:
|
[9] H. H. Storrer: ARRAY(0x9afdfe8).Lecture Notes in Math. vol. 246, Springer-Verlag, New York, 1992, pp. 617–661. MR 0360717 |
| Reference:
|
[10] R. Wisbauer: Foundations of Module and Ring Theory.Gordon and Breach. Reading, 1991. Zbl 0746.16001, MR 1144522 |
| . |
