Literature cited
C. U. Jensen, “A remark on arithmetical rings,” Proc. Am. Math. Soc.,15, No. 6, 951–954 (1964).
N. I. Dubrovin, “An example of a chain prime ring with nilpotent elements,” Mat. Sb.,120, No. 3, 441–447 (1983).
N. Bourbaki, Commutative Algebra, Addison-Wesley (1972).
Y. Hinohara, “Note on noncommutative local rings,” Nagoya Math. J.,17, 161–166 (1960).
C. Faith, Algebra: Rings, Modules, and Categories. Vol. 1, Springer-Verlag (1973).
V. A. Andrunakievich and Yu. M. Ryabukhin, Radicals of Algebras and Structure Theory [in Russian], Nauka, Moscow (1979).
W. Stephenson, “Modules whose lattice of submodules is distributive,” Proc. London Math. Soc.,28, No. 2, 291–310 (1974).
A. A. Tuganbaev, “Distributive Noetherian rings,” Vestn. Mosk. Gos. Univ., Ser. 1, Matematika, Mekhanika, No. 2, 30–35 (1980).
B. Stenström, Rings of Quotients, Springer-Verlag, Berlin (1975).
A. A. Tuganbaev, “Distributive modules,” Usp. Mat. Nauk,35, No. 5, 245–246 (1980).
J. Goursaud and J. L. Pascaud, “Anneaux de polynômes semi-hereditaires,” in: Lecture Notes in Math.,734 (1979), pp. 131–157.
P. M. Cohn, Free Rings and Their Relations, Academic Press (1972).
A. A. Tuganbaev, “Distributive modules and rings,” Usp. Mat. Nauk,39, No. 1, 157–158 (1984).
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Translated from Matematicheskie Zametki, Vol. 38, No. 2, pp. 218–228, August, 1985.
The author is grateful to A. V. Mikhalev for valuable advice.
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Tuganbaev, A.A. Rings with flat right ideals and distributive rings. Mathematical Notes of the Academy of Sciences of the USSR 38, 631–636 (1985). https://doi.org/10.1007/BF01156242
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DOI: https://doi.org/10.1007/BF01156242