On some classes of modules
Czechoslovak Mathematical Journal, Tome 50 (2000) no. 4, pp. 839-846 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 16D10, 16D80, 16D99
Keywords: quasi-corational module; copolyform module; $\alpha $-coatomic module
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Güngöroglu, Gonca; Harmanci, Abdullah. On some classes of modules. Czechoslovak Mathematical Journal, Tome 50 (2000) no. 4, pp. 839-846. http://geodesic.mathdoc.fr/item/CMJ_2000_50_4_a10/

[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

[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 | MR

[4] F. Kasch: Modules and Rings. Academic Press, 1982. | MR | Zbl

[5] D. Kirby: Dimension and length for artinian modules. Quart. J. Math. Oxford Ser. 2 41 (1990), 419–429. | DOI | MR | Zbl

[6] S. H. Mohammed and B. J. Muller: Continuous and Discrete Modules. London Math. Soc. Lecture Notes 147, Cambridge Univ. Press, 1990. | MR

[7] K. Oshiro: Semiperfect modules and quasi-semiperfect modules. Osaka J. Math. 20 (1983), 337–372. | MR | Zbl

[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 | MR | Zbl

[9] H. H. Storrer: ARRAY(0x9afdfe8). Lecture Notes in Math. vol. 246, Springer-Verlag, New York, 1992, pp. 617–661. | MR

[10] R. Wisbauer: Foundations of Module and Ring Theory. Gordon and Breach. Reading, 1991. | MR | Zbl