论文信息 - Rings whose class of projective modules is socle fine

Rings whose class of projective modules is socle fine

A class C of modules over a unitary ring is said to be socle fine if whenever M, N ∈ C with Soc(M) ∼= Soc(N) then M ∼= N. In this work we characterize certain types of rings by requiring a suitable class of its modules to be socle fine. Then we study socle fine classes of quasi-injective, quasi-projective and quasicontinuous modules which we apply to find socle fine classes in special types of noetherian rings. We also initiate the study of those rings whose class of projective modules is socle fine.

D. M. Barquero | C. M. González | A. Idelhadj | E. A. Kaidi

[1] Abdelouahab Idelhadj,et al. Nouvelles caracterisations des v-anneaux et des anneaux pseudo-frobeniusiens 1 , 1995 .

[2] Yiqiang Zhou,et al. Direct sums of quasi-injective modules, injective covers, and natural classes , 1994 .

[3] Saad H. Mohamed,et al. Continuous and Discrete Modules , 1990 .

[4] Sergio R. López-Permouth,et al. Rings whose cyclics are essentially embeddable in projective modules , 1990 .

[5] S. Rizvi. Commutative rings for which every continuous module is quasi-injective , 1988 .

[6] F. Kasch,et al. Modules and rings , 1982 .

[7] Carl Faith,et al. Algebra II: Ring Theory , 1976 .

[8] H. Schwetlick. Wilkinson, J. H. and C. Reinsch, Linear Algebra. (Die Grundlehren der mathematischen Wissenschaften, Band 186). X + 439 S. m. 4 Fig. Vol. II. Berlin/Heidelberg/New York 1971. Springer‐Verlag. Preis geb. DM 72,— , 1975 .

[9] Frank W. Anderson,et al. Rings and Categories of Modules , 1974 .

[10] A. Koehler. QUASI-PROJECTIVE COVERS AND DIRECT SUMS , 1970 .

[11] J. Golan. Characterization of rings using quasiprojective modules , 1970 .

[12] M. Harada. Note on quasi-injective modules , 1965 .

[13] H. Bass. Finitistic dimension and a homological generalization of semi-primary rings , 1960 .

[14] N. Jacobson. Structure of rings , 1956 .

[15] I. Kaplansky. Modules over Dedekind rings and valuation rings , 1952 .