Abstract
We study rings over which all right modules are I 0-modules.
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A. N. Abyzov, “Closure of weakly regular modules with respect to direct sums,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 9, 3–5 (2003).
A. N. Abyzov, “Weakly regular modules over semiperfect rings,” Chebyshevskii Sb., 4, No. 1, 4–9 (2003).
A. N. Abyzov, “Weakly regular modules,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 3, 3–6 (2004).
C. Faith, Algebra: Rings, Modules, and Categories, Vol. I, Springer, Berlin (1973).
C. Faith, Algebra II, Ring Theory, Springer, Berlin (1976).
H. Hamza, “I 0-rings and I 0-modules,” Math. J. Okayama Univ., 40, 91–97 (1998).
Kh. I. Khakmi, “Strongly regular and weakly regular rings and modules,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 5, 60–65 (1994).
W. K. Nicholson, “I-rings,” Trans. Amer. Math. Soc., 207, 361–373 (1975).
W. K. Nicholson, “Semiregular modules and rings,” Can. J. Math., 28, No. 5, 1105–1120 (1976).
W. K. Nicholson and M. F. Yousif, Quasi-Frobenius Rings, Cambridge Univ. Press, Cambridge (2003).
A. Tuganbaev, Rings Close to Regular, Kluwer Academic, Dordrecht (2002).
A. A. Tuganbaev, “Semiregular, weakly regular, and π-regular rings,” J. Math. Sci., 109, No. 3, 1509–1588 (2002).
R. Wisbauer, Foundations of Module and Ring Theory, Gordon and Breach, Philadelphia (1991).
W. M. Xue, “Semiregular modules and F-semiperfect modules,” Comm. Algebra, 23, No. 3, 1035–1046 (1995).
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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 8, pp. 233–241, 2006.
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Tuganbaev, A.A. Modules with many direct summands. J Math Sci 152, 298–303 (2008). https://doi.org/10.1007/s10958-008-9053-z
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DOI: https://doi.org/10.1007/s10958-008-9053-z