Previous |  Up |  Next


quasi-corational module; copolyform module; $\alpha $-coatomic module
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.
[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
[2] F. W. Anderson and K. R. Fuller: Rings and Categories. Springer-Verlag, New York, 1973.
[3] R. Courter: Finite direct sums of complete matrix rings over perfect completely primary rings. Canad. J. Math. 21 (1968), 430–446. DOI 10.4153/CJM-1969-047-0 | MR 0257141
[4] F. Kasch: Modules and Rings. Academic Press, 1982. MR 0667346 | Zbl 0523.16001
[5] D. Kirby: Dimension and length for artinian modules. Quart. J. Math. Oxford Ser. 2 41 (1990), 419–429. DOI 10.1093/qmath/41.4.419 | MR 1081104 | Zbl 0724.13015
[6] S. H. Mohammed and B. J. Muller: Continuous and Discrete Modules. London Math. Soc. Lecture Notes 147, Cambridge Univ. Press, 1990. MR 1084376
[7] K. Oshiro: Semiperfect modules and quasi-semiperfect modules. Osaka J. Math. 20 (1983), 337–372. MR 0706241 | Zbl 0516.16015
[8] R. N. Roberts: Krull dimension for Artinian modules over quasi-local commutative Rings. Quart. J. Math. Oxford Ser. 3 26 (1975), 269–273. DOI 10.1093/qmath/26.1.269 | MR 0389884 | Zbl 0311.13006
[9] H. H. Storrer: ARRAY(0x9afdfe8). Lecture Notes in Math. vol. 246, Springer-Verlag, New York, 1992, pp. 617–661. MR 0360717
[10] R. Wisbauer: Foundations of Module and Ring Theory. Gordon and Breach. Reading, 1991. MR 1144522 | Zbl 0746.16001
Partner of
EuDML logo