Non-perfect rings and a theorem of Eklof and Shelah

Jan Trlifaj

Commentationes Mathematicae Universitatis Carolinae (1991)

  • Volume: 32, Issue: 1, page 27-32
  • ISSN: 0010-2628

Abstract

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We prove a stronger form, , of a consistency result, , due to Eklof and Shelah. concerns extension properties of modules over non-left perfect rings. We also show (in ZFC) that does not hold for left perfect rings.

How to cite

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Trlifaj, Jan. "Non-perfect rings and a theorem of Eklof and Shelah." Commentationes Mathematicae Universitatis Carolinae 32.1 (1991): 27-32. <http://eudml.org/doc/247272>.

@article{Trlifaj1991,
abstract = {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.},
author = {Trlifaj, Jan},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {perfect ring; Ext; uniformization; -free module; projective module; consistency; extension properties; Whitehead property; ZFC; left perfect rings},
language = {eng},
number = {1},
pages = {27-32},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Non-perfect rings and a theorem of Eklof and Shelah},
url = {http://eudml.org/doc/247272},
volume = {32},
year = {1991},
}

TY - JOUR
AU - Trlifaj, Jan
TI - Non-perfect rings and a theorem of Eklof and Shelah
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1991
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 32
IS - 1
SP - 27
EP - 32
AB - 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.
LA - eng
KW - perfect ring; Ext; uniformization; -free module; projective module; consistency; extension properties; Whitehead property; ZFC; left perfect rings
UR - http://eudml.org/doc/247272
ER -

References

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  1. Anderson F.W., Fuller K.R., Rings and Categories of Modules, Springer, New York 1974. Zbl0765.16001MR0417223
  2. Eklof P.C., Set Theoretic Methods in Homological Algebra and Abelian Groups, Montreal Univ. Press, Montreal 1980. Zbl0669.03022MR0565449
  3. Eklof P.C., Shelah S., On Whitehead modules, preprint 1990. Zbl0743.16004MR1127077
  4. Shelah S., Diamonds, uniformization, J. Symbolic Logic 49 (1984), 1022-1033. (1984) Zbl0598.03044MR0771774
  5. Trlifaj J., Von Neumann regular rings and the Whitehead property of modules, Comment. Math. Univ. Carolinae 31 (1990), 621-625. (1990) Zbl0728.16005MR1091359
  6. Trlifaj J., Associative Rings and the Whitehead Property of Modules, R. Fischer, Munich 1990. Zbl0697.16024MR1053965

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