Publications and Preprints for Ian M. Aberbach

    1. Test elements in excellent rings with an application to the Uniform Artin-Rees property,
    2. Proc. A. M.S.,  118   (1993), 355-363.
    3. (with M. Hochster and C. Huneke)   Localization of tight closure and modules of finite phantom projective dimension,
    4. J. reine angew. Math.,  434 (1993),  67--114.
    5. Finite phantom projective dimension,  Amer. J. Math., 116   (1994), 447-477.
    6. (with C. Huneke)    An improved Briancon-Skoda theorem with applications to the Cohen-Macaulayness of
    7. Rees rings,  Math. Ann.,    297   (1993),   343--369.
    8. Tight closure in  F-rational rings,  Nagoya J. of Math., 135   (1994), 43-54.
    9. (with S. Huckaba and C. Huneke)     Reduction numbers, Rees rings, and Pfaffian ideals,
    10. J. Pure and Appl. Alg.,   23  (1995),  2003-2026.
    11. (with C. Huneke and N. V. Trung)    Reduction numbers, Briancon-Skoda theorems and the depth of Rees rings,
    12. Comp. Math.,    97   (1995),   403-434.
    13. (with S. Huckaba)   Reduction number bounds on analytic  deviation two ideals and Cohen-Macaulayness
    14. of associated graded rings, Comm in Alg.,   23  (1995),   2003-2026.
    15. (with C. Huneke)   A theorem of Briancon-Skoda type for regular rings containing a field,
    16. Proc. Amer. Math. Soc.,   124   (1996),   707--713.
    17. (with M. Hochster)    Finite Tor dimension and failure of coherence in absolute integral closures,
    18. J. Pure Appl. Alg.,    122  (1997),  171--184.
    19. Local reduction numbers and Cohen-Macaulayness of associated graded rings,
    20. J. of Alg.,   178  (1995),  833--842.
    21. Cohen-Macaulay associated graded rings for ideals which are not generic complete intersections,
    22. Comm. in Alg.,    23   (1995),  4509--4520.
    23. (with C. Huneke and K.E. Smith)    A tight closure approach to arithmetic  Macaulayfication,
    24. Ill. J. Math.,    40   (1996),   310--329.
    25. Arithmetic Macaulayfications using ideals of dimension one,
    26. Ill. J. Math.,    40   (1996), 518--526.
    27. (with M. Katzman and B. MacCrimmon)  Weak F-regularity deforms in Q-Gorenstein rings,
    28. J. Alg.,    204  (1998),  281--285.
    29. Some conditions for the equivalence of weak and strong F-regularity,
    30. Comm. Algebra 30 (2002), no. 4, 1635--1651.
    31. (with C. Huneke)   F-rational rings and the integral closure of ideals,
    32. Mich. Math. J.,  49  (2001),  3--11  ( arXiv ).
    33. Extension of weakly and strongly F-regular rings by flat maps,
    34. J. Alg.,    241   (2001), 799--807 ( arXiv ).
    35. (with C. Huneke)   F-rational rings and the integral closure of ideals II,
    36. in Ideal Theoretic Methods in Commutative Algebra,
      Lecture notes in pure and applied mathematics    220  (2001), Marcel Dekker,  1--12.
    37. (with F. Enescu)   Test ideals and base  change problems in tight closure theory,  Trans. A. M. S.,   355 (2003), no. 2, 619--636. (ps , arXiv)
    38. (with G. L. Leuschke)  The F-signature and strong F-regularity, Math. Res. Letters,  10 (2003), no. 1, 51--56. MR 1 960 123  (ps , arXiv)
    39. (with L. Ghezzi and T. Ha)   The depth of the associated graded ring of ideals with any reduction number,   J. Algebra 276 (2004), no. 1, 168--179 (ps, arXiv)
    40. The vanishing of Tor_1^R(R^+, k) implies that R is regular,  Proc. Amer. Math. Soc. 133 (2004) 27-29.  (arXiv)
    41. (with F. Enescu) The structure of F-pure rings, Math. Zeit., 250 (2005), 791--806.   math.AC/0310227
    42. (with L. Ghezzi and T. Ha) Homology Multipliers and the relation type of parameter ideals, Pacific Journal of Math.,
      226  (2006),  1--39.   math.AC/0501477
    43. (with F. Enescu)  When does the F-signature exist?, Annales de la Faculte des Sciences de Toulouse,
      15 (2006),  195--201.  math.AC/0502351 .
    44. The existence of the F-signature for rings with large Q-Gorenstein locus, submitted.
    45. (with F. Enescu) Lower bounds for Hilbert-Kunz multiplicities in local rings of fixed dimension,
      submitted.