Geodesic
Rings over which all modules are semiregular
Fundamentalʹnaâ i prikladnaâ matematika, Tome 13 (2007) no. 2, pp. 185-194.

Voir la notice de l'article provenant de la source Math-Net.Ru

For a ring $A$, it is proved that all $A$\df modules are semiregular if and only if $A$ is an Artinian serial ring and $J^2(A)=0$. 
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A. A. Tuganbaev. Rings over which all modules are semiregular. Fundamentalʹnaâ i prikladnaâ matematika, Tome 13 (2007) no. 2, pp. 185-194. http://geodesic.mathdoc.fr/item/FPM_2007_13_2_a7/

[1] Abyzov A. N., “Zamknutost slabo regulyarnye modulei otnositelno pryamykh summ”, Izv. vyssh. uchebn. zaved. Matematika, 2003, no. 9, 3–5 | MR

[2] Abyzov A. N., “Slabo regulyarnye moduli nad polusovershennymi koltsami”, Chebyshëvskii sb., 4:1 (2003), 4–9 | MR | Zbl

[3] Abyzov A. N., “Slabo regulyarnye moduli”, Izv. vyssh. uchebn. zaved. Matematika, 2004, no. 3, 3–6 | MR | Zbl

[4] Feis K., Algebra: koltsa, moduli i kategorii, t. 2, Mir, M., 1979 | MR

[5] Khakmi Kh. I., “Silno regulyarnye i slabo regulyarnye koltsa i moduli”, Izv. vyssh. uchebn. zaved. Matematika, 1994, no. 5, 60–65 | MR | Zbl

[6] Hamza H., “$I_0$-rings and $I_0$-modules”, Math. J. Okayama Univ., 40 (1998), 91–97 | MR

[7] Nicholson W. K., “$I$-rings”, Trans. Amer. Math. Soc., 207 (1975), 361–373 | DOI | MR | Zbl

[8] Nicholson W. K., “Semiregular modules and rings”, Can. J. Math., 28:5 (1976), 1105–1120 | DOI | MR | Zbl

[9] Nicholson W. K., Yousif M. F., Quasi-Frobenius Rings, Cambridge Univ. Press, Cambridge, 2003 | MR | Zbl

[10] Osofsky B. L., “Rings all of whose finitely generated modules are injective”, Pacific J. Math., 14 (1964), 645–650 | MR | Zbl

[11] Tuganbaev A., Rings Close to Regular, Kluwer Academic, Dordrecht, 2002 | MR | Zbl

[12] Tuganbaev A. A., “Semiregular, weakly regular, and $\pi$-regular rings”, J. Math. Sci., 109:3 (2002), 1509–1588 | DOI | MR | Zbl

[13] Vanaja N., Purav V. M., “Characterization of generalized uniserial rings in terms of factor rings”, Comm. Algebra, 20 (1992), 2253–2270 | DOI | MR | Zbl

[14] Wisbauer R., Foundations of Module and Ring Theory, Gordon and Breach, Philadelphia, 1991 | MR | Zbl

[15] Xue W. M., “Semiregular modules and $F$-semiperfect modules”, Comm. Algebra, 23:3 (1995), 1035–1046 | DOI | MR | Zbl