University of California, Irvine

Department of Mathematics

Professor Emeritus Paul C. Eklof



Department of Mathematics
Irvine, CA 92697-3875













  • Baer modules over domains (with L. Fuchs and S. Shelah), Transactions of Amer. Math. Soc., 322 (1990), 547-560.
  • Almost Free Modules: Set-theoretic methods, (with A. Mekler), North-Holland Publishing Company (1990), 482 pages.
  • On Whitehead Modules (with S. Shelah), J. of Algebra 142 (1991), 492-510.
  • A transfer theorem for non-standard uniserials, Proceedings of Amer. Math. Soc. 114 (1992), 593-600.
  • Set-theoretic methods: the uses of Gamma invariants, in Abelian Groups, the proceedings of the Curaçao conference on torsion-free abelian groups, Lecture Notes in Pure and Applied Math. No. 146, Marcel Dekker (1993), 143-153.
  • On a conjecture regarding non-standard uniserial modules (with S. Shelah), Trans. Amer. Math. Soc., 140 (1993), 337-351.
  • Uniformization and the diversity of Whitehead groups (with A. Mekler and S. Shelah), Israel J. Math. 80 (1992), 301-321.
  • Explicitly non-standard uniserial modules (with S. Shelah), J. Pure and Applied Algebra, 86 (1993), 35-50.
  • Hereditarily separable groups and monochromatic uniformization (with A. Mekler and S. Shelah), Israel J. Math., 88 (1994), 213-235.
  • Model theory of modules over a serial ring (with I. Herzog), Annals of Pure and App. Logic 72 (1995), 145-176.
  • A combinatorial principle equivalent to the existence of non-free Whitehead groups (with S. Shelah), in Abelian Group Theory and Related Topics, Contemporary Math. v. 171 (1994), 79-98.
  • On invariants for w1-separable groups (with M. Foreman and S. Shelah), Trans. Amer. Math. Soc. 347 (1995), 4385-4402.
  • Torsion modules, lattices and p-points (with B. Huisgen-Zimmermann and S. Shelah), Bulletin of London Math. Soc. 29(1997), 547-555.
  • Set theory generated by abelian group theory, Bulletin of Symbolic Logic, 3 (1997), 1-16.
  • The Kaplansky test problems for N1-separable groups (with S. Shelah), Proc. Amer Math. Soc. 126(1998), 1901-1907.
  • Gamma invariants for dense lattices (with J. Trlifaj), Algebra Universalis, 40 (1998), 427-445.
  • Absolutely rigid systems and absolutely indecomposable groups (with S. Shelah),in Abelian Groups and Modules (ed. P. Eklof and R. Goebel), Birkhaeuser (1999), 257-268. Correction
  • A non-reflexive Whitehead group (with S. Shelah), J. of Pure and Applied Algebra 156 (2001), 199-214.
  • Modules with strange decomposition properties , in Infinite Length Modules (ed. H. Krause and C. M. Ringel), Birkhaeuser, 75-87.
  • How to make Ext vanish (with J. Trlifaj), Bull. London Math. Soc. 33 (2001), 41-51.
  • Covers induced by Ext (with J. Trlifaj), J. Algebra 231 (2000), 640-651.
  • Whitehead modules, invited chapter for Handbook of Algebra (ed. M. Hazewinkel), volume 3 (2003), 317-341 (Elsevier)
  • The structure of Ext (A,Z) and GCH: possible co-Moore spaces (with S. Shelah), Math. Zeit. 239 (2002), 143-157.
  • Whitehead modules over large principal ideal domains (with S. Shelah), Forum Math. 14 (2002), 477-482.
  • The affinity of set theory and abelian group theory , Rocky Mt. J., 32 (2002), 1119--1134.
  • Almost Free Modules: Set-theoretic methods, Revised edition , North-Holland Mathematical Library vol. 65 (2002), 597 pages. Errata (errata.pdf)  Update on open problems open_update.pdf
  • On the existence of precovers (with S. Shelah), Illinois J. Math. 47(2003), 173-188.
  • On the cogeneration of cotorsion pairs (with S. Shelah and J. Trlifaj), J. Algebra 277 (2004), 572--578.
  • Tilting cotorsion pairs (with S. Bazzoni and J. Trlifaj), Bull. London Math. Soc. 37 (2005), 683—696..
  • Test groups for Whitehead groups (with L. Fuchs and S. Shelah), Rocky Mt. J. Math, to appear.Whtest.pdf
  • N as an abstract elementary class (with J. Baldwin and J. Trlifaj), Annals of Pure and App. Logic 149 (2007), 25-39, Nperp-aec.pdf
  • Shelah's Singular Compactness Theorem, Publicacions Matematiques 52 (2008), 3-18 SingComp.pdf

Return to Faculty page
Return to Mathematics ->