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Article

Trlifaj, Jan
Non-perfect rings and a theorem of Eklof and Shelah. (English). Commentationes Mathematicae Universitatis Carolinae, vol. 32 (1991), issue 1, pp. 27-32
MSC: 03E55, 16A50, 16A51, 16D40, 16L30 | MR 1118286 | Zbl 0742.16001
Keywords:
perfect ring; Ext; uniformization
Summary:
We prove a stronger form, $A^+$, of a consistency result, $A$, due to Eklof and Shelah. $A^+$ concerns extension properties of modules over non-left perfect rings. We also show (in ZFC) that $A$ does not hold for left perfect rings.
References:
[1] Anderson F.W., Fuller K.R.: Rings and Categories of Modules. Springer, New York 1974. MR 0417223 | Zbl 0765.16001
[2] Eklof P.C.: Set Theoretic Methods in Homological Algebra and Abelian Groups. Montreal Univ. Press, Montreal 1980. MR 0565449 | Zbl 0669.03022
[3] Eklof P.C., Shelah S.: On Whitehead modules. preprint 1990. MR 1127077 | Zbl 0743.16004
[4] Shelah S.: Diamonds, uniformization. J. Symbolic Logic 49 (1984), 1022-1033. MR 0771774 | Zbl 0598.03044
[5] Trlifaj J.: Von Neumann regular rings and the Whitehead property of modules. Comment. Math. Univ. Carolinae 31 (1990), 621-625. MR 1091359 | Zbl 0728.16005
[6] Trlifaj J.: Associative Rings and the Whitehead Property of Modules. R. Fischer, Munich 1990. MR 1053965 | Zbl 0697.16024
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