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References
B. Brown andN. H. McCoy, The maximal regular ideal of a ring. Proc. Amer. Math. Soc.1, 165–171 (1950).
C. Faith, Rings with minimum condition on principal ideals II. Arch. Math.12, 179–181 (1961).
C.Faith, Algebra II: Ring Theory. Grundlehren Math. Wiss.191, Berlin-New York-Heidelberg 1976.
C. Faith, Injective quotient rings of commutative rings. LNM700, 151–203, Berlin 1979.
C.Faith and S.Page, FPF Ring Theory: Faithful Modules and Generators of Mod-R. Lecture Notes London Math. Soc., Cambridge-London-New York-New Rochelle-Melbourne-Sydney 1984.
C. Faith andY. Utumi, Quasi-injective modules and their endomorphism rings. Arch. Math.15, 266–270 (1964).
C. Faith, On a new proof of Litoff's theorem. Acta. Math. Acad. Sci. Hungar.14, 369–371 (1963).
M. Hall, Jr., The position of the radical of an algebra. Trans. Amer. Math. Soc.48, 391–404 (1940).
M. Harada, Note on quasi-injective modules. Osaka J. Math.2, 351–356 (1965).
I. Kaplansky, Topological representation of algebras II. Trans Amer. Math. Soc.68, 62–75 (1950).
B. L. Osofsky, Endomorphism rings of quasi-injective modules. Canad. J. Math.20, 895–903 (1968).
Y. Utumi, On continuous rings and self-injective rings. Trans. Amer. Math. Soc.118, 158–173 (1965).
Y. Utumi, On self-injective rings. J. Algebra6, 56–64 (1967).
C. Faith, Subrings of self-injective and FPF rings. LNM951, 12–20, Berlin 1982.
C.Faith, Maximal regular subrings of self-injective rings. Submitted.
S. Page, On regular FPF rings. Pacific J. Math79, 169–176 (1978).
S. Page, Corrections and Addendum to [16], Pacific J. Math.97, 488–490 (1981).
B. Zimmerman-Huisgen andW. Zimmerman, Algebraically compact rings and modules. Math. Z.161, 81–93 (1978).
B.Zimmerman, Direct products of modules and algebraic compactness. Tech. U. München (TUM) 1980.
M. Henriksen, Two classes of rings generated by their units. J. Algebra31, 182–193 (1974).
K. R.Goodearl, Von Neumann Regular Rings. London-San Francisco-Melbourne 1979.
Y. Utumi, On the continuity and self-injectivity of a complete regular ring. Canad. J. Math.18, 404–412 (1966).
Y. Utumi, On continuous regular rings. Canad. Math. Bull.4, 63–69 (1961).
N.Jacobson, The Structure of Rings. Amer. Math. Soc., Providence, 1956, 1964 (revised).
A. W. Chatters andC. R. Hajarnavis, Rings in which every complement right ideal is a direct summand. Quart. J. Math. Oxford Ser. (2)28, no. 109, 61–80 (1977).
D. Van Huynh, On the maximal regular ideal of a linearly compact ring. Arch. Math.33, 232–234 (1979).
C. Faith, Injective quotient rings of commutative rings II. In Injective Modules and Injective Quotient Rings. LN Pure App. Math.72, 71–105 (1982).
B. Mueller, On injective and quasi-continuous modules. J. Pure Appl. Algebra28, 197–210 (1983).
I.Kaplansky, Infinite Abelian Groups. Ann Arbor rev. ed. 1969.
F. L.Sandomiérski, Linearly compact modules and local Morita duality, in Ring Theory. New York-London 1972.
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For N. H. McCoy, Professor Emeritus, Smith College
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Faith, C. The maximal regular ideal of self-injective and continuous rings splits off. Arch. Math 44, 511–521 (1985). https://doi.org/10.1007/BF01193991
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DOI: https://doi.org/10.1007/BF01193991