Publications of R. Y. Sharp

Books

  1. Commutative algebra: Durham 1981 (Ed. R.Y. Sharp), London Mathematical Society Lecture Note Series 72 (Cambridge University Press, Cambridge, 1982), 250pp.
  2. Steps in commutative algbera, London Mathematical Society Student Texts 19 (Cambridge University Press, Cambridge, 1990), 321pp.
  3. (M.P. Brodmann and R.Y. Sharp) Local cohomology: an algebraic introduction with geometric applications, Cambridge Studies in Advanced Mathematics 60 (Cambridge University Press, Cambridge, 1998), 416pp.
  4. Steps in commutative algbera: second edition London Mathematical Society Student Texts 51 (Cambridge University Press, Cambridge, 2000), 355pp.

Papers

  1. The Cousin complex for a module over a commutative Noetherian ring, Math. Zeit., 112 (1969), 340-356.
  2. Gorenstein modules, Math. Zeit., 115 (1970), 117-139.
  3. Local cohomology theory in commutative algebra, Quart. J. Math. Oxford (2), 21 (1970), 425-434.
  4. Cousin complex characterizations of two classes of commutative Noetherian rings, J. London Math. Soc. (2), 3 (1971), 621-624.
  5. On Gorenstein modules over a complete Cohen-Macaulay local ring, Quart. J. Math. Oxford (2), 22 (1971), 425-434.
  6. (I.G. Macdonald and R.Y. Sharp) An elementary proof of the non-vanishing of certain local cohomology modules, Quart. J. Math. Oxford (2), 23 (1972), 197-204.
  7. Finitely generated modules of finite injective dimension over certain Cohen-Macaulay rings", Proc. London Math. Soc. (3), 25 (1972), 303-328.
  8. The Euler characteristic of a finitely generated module of finite injective dimension, Math. Zeit., 130 (1973), 79-93.
  9. The Cousin complex and integral extensions of Noetherian domains, Proc. Camb. Phil. Soc., 73 (1973), 407-415.
  10. The construction of a module of finite projective dimension from a finitely generated module of finite injective dimension, Comment. Math. Helvetici, 50 (1975), 15-26.
  11. A note on Northcott's work on generalized Koszul complexes and Artinian modules, Quart. J. Math. Oxford (2), 26 (1975), 19-22.
  12. Some results on the vanishing of local cohomology modules, Proc. London Math. Soc. (3), 30 (1975), 177-195.
  13. Ramification indices and injective modules, J. London Math. Soc. (2), 11 (1975), 267-275.
  14. Dualizing complexes for commutative Noetherian rings, Math. Proc. Camb. Phil. Soc., 78 (1975), 369-386.
  15. The effect on associated prime ideals produced by an extension of the base field, Math. Scand., 38 (1976), 43-52.
  16. Secondary representations for injective modules over commutative Noetherian rings, Proc. Edinburgh Math. Soc., 20 (1976), 143-151.
  17. Acceptable rings and homomorphic images of Gorenstein rings, J. Algebra, 44 (1977), 246-261.
  18. Local cohomology and the Cousin complex for a commutative Noetherian ring, Math. Zeit., 153 (1977), 19-22.
  19. The dimension of the tensor product of two field extensions, Bull. London Math. Soc., 9 (1977), 42-48.
  20. Simplifications in the theory of tensor products of field extensions, J. London Math. Soc. (2), 15 (1977), 48-50.
  21. A note on the dimensions of commutative Noetherian domains, J. London Math. Soc. (2), 15 (1977), 415-418.
  22. A commutative Noetherian ring which possesses a dualizing complex is acceptable, Math. Proc. Camb. Phil. Soc., 82 (1977), 197-213.
  23. On the fibre rings of a formal power series extension, Quart. J. Math. Oxford (2), 28 (1977), 487-494.
  24. (R.Y. Sharp and P. Vámos) The dimension of the tensor product of a finite number of field extensions, J. Pure and Applied Algebra, 10 (1977), 249-252.
  25. (Janet E. Hall and R.Y. Sharp) Dualizing complexes and flat homomorphisms of commutative Noetherian rings, Math. Proc. Camb. Phil. Soc., 84 (1978), 37-45.
  26. (D. Rees and R.Y. Sharp) On a theorem of B. Teissier on multiplicities of ideals in local rings, J. London Math. Soc. (2), 18 (1978), 449-463.
  27. (M.H. Bijan-Zadeh and R.Y. Sharp) On Grothendieck's local duality theorem, Math. Proc. Camb. Phil. Soc., 85 (1979), 431-437.
  28. (Janet E. Hall and R.Y. Sharp) Duality for a commutative Noetherian ring which possesses a dualizing complex, Quart. J. Math. Oxford (2), 30 (1979), 283-299.
  29. Necessary conditions for the existence of dualizing complexes in commutative algebra, Springer Lecture Notes in Math., 740 (1979), 213-229.
  30. On the attached prime ideals of certain Artinian local cohomology modules, Proc. Edinburgh Math. Soc., 24 (1981), 9-14.
  31. Cohen-Macaulay properties for balanced big Cohen-Macaulay modules, Math. Proc. Camb. Phil. Soc., 90 (1981), 229-238.
  32. (R.Y. Sharp and H. Zakeri) Modules of generalized fractions, Mathematika, 29 (1982), 32-41.
  33. A Cousin complex characterization of balanced big Cohen-Macaulay modules, Quart. J. Math. Oxford (2), 33 (1982), 471-485.
  34. (R.Y. Sharp and H. Zakeri) Local cohomology and modules of generalized fractions, Mathemetika, 29 (1982), 296-306.
  35. (R.Y. Sharp and H. Zakeri) Modules of generalized fractions and balanced big Cohen-Macaulay modules, London Mathematical Society Lecture Notes, 72 (1982), 61-82.
  36. On the structure of certain exact Cousin complexes, Marcel Dekker Lecture Notes in Pure and Applied Mathematics, 84 (1983), 275-290.
  37. (A.M. Riley, R.Y. Sharp and H. Zakeri) Cousin complexes and generalized fractions, Glasgow Math. J., 26 (1985), 51-67.
  38. (R.Y. Sharp and H. Zakeri) Generalized fractions and the monomial conjecture, J. Algebra, 92 (1985), 380-388.
  39. (R.Y. Sharp and P. Vámos) Baire's category theorem and prime avoidance in complete local rings, Archiv der Math., 44 (1985), 243-248.
  40. (M.A. Hamieh and R.Y. Sharp) Krull dimension and generalized fractions, Proc. Edinburgh Math. Soc., 28 (1985), 349-353.
  41. (R.Y. Sharp and M.A. Hamieh) Lengths of certain generalized fractions, J. Pure and Applied Algebra, 38 (1985), 323-336.
  42. (R.Y. Sharp and H. Zakeri) Generalized fractions, Buchsbaum modules, and generalized Cohen-Macaulay modules, Math. Proc. Camb. Phil. Soc., 98 (1985), 429-436.
  43. (F.W. Call and R.Y. Sharp) A short proof of the local Lichtenbaum-Hartshorne Theorem on the vanishing of local cohomology, Bull. London Math. Soc., 18 (1986), 261-264.
  44. Asymptotic behaviour of certain sets of attached prime ideals, J. London Math. Soc. (2), 34 (1986), 212-218.
  45. (R.Y. Sharp and A.-J. Taherizadeh) Reductions and integral closures of ideals relative to an Artinian module, J. London Math. Soc. (2), 37 (1988), 203-218.
  46. A method for the study of Artinian modules, with an application to asymptotic behavior, Springer Mathematical Sciences Research Institute Publications, 15 (1989), 443-465.
  47. Certain countably generated big Cohen-Macaulay modules are balanced, Math. Proc. Camb. Phil. Soc., 105 (1989), 73-77.
  48. (R.Y. Sharp and M. Yassi) Generalized fractions and Hughes' grade-theoretic analogue of the Cousin complex, Glasgow Math. J., 32 (1990), 173-188.
  49. (R.Y. Sharp, Y. Tiras and M. Yassi) Integral closures of ideals relative to local cohomology modules over quasi-unmixed local rings, J. London Math Soc. (2), 42 (1990), 385-392.
  50. (H. Ansari Toroghy and R.Y. Sharp) Asymptotic behaviour of ideals relative to injective modules over commutative Noetherian rings, Proc. Edinburgh Math. Soc., 34 (1991), 155-160.
  51. The Frobenius homomorphism, and local cohomology in regular local rings of positive characteristic, J. Pure and Applied Algebra, 71 (1991), 313-317.
  52. (H. Ansari Toroghy and R.Y. Sharp) Integral closures of ideals relative to injective modules over commutative Noetherian rings, Quart. J. Math. Oxford (2), 42 (1991), 393-402.
  53. (R.Y. Sharp and Y. Tiras) Integral closures of ideals relative to Artinian modules, and exact sequences, Glasgow Math. J., 34 (1992), 103-107.
  54. Artinian modules over commutative rings, Math. Proc. Camb. Phil. Soc., 111 (1992), 25-33.
  55. (H. Ansari Toroghy and R.Y. Sharp) Asymptotic behaviour of ideals relative to injective modules over commutative Noetherian rings II, Proc. Edinburgh Math. Soc., 35 (1992), 511-518.
  56. (R.Y. Sharp and Y. Tiras) Asymptotic behaviour of integral closures of ideals relative to Artinian modules, J. Algebra, 153 (1992), 262-269.
  57. (R.Y. Sharp and Zhongming Tang) On the structure of Cousin complexes, J. Math. Kyoto Univ., 33 (1993), 285-297.
  58. (C.L. Huneke and R.Y. Sharp) Bass numbers of local cohomology modules, Transactions Amer. Math. Soc., 339 (1993), 765-779.
  59. (R.Y. Sharp and P. Schenzel) Cousin complexes and generalized Hughes complexes, Proc. London Math. Soc. (3), 68 (1994), 499-517.
  60. (R.Y. Sharp and M. Tousi) Comparison of complexes of modules of generalized fractions and generalized Hughes complexes, Glasgow Math. J., 37 (1995), 55-64.
  61. (R.Y. Sharp and M. Tousi) A characterization of generalized Hughes complexes, Math. Proc. Camb. Phil. Soc., 120 (1996), 71-85.
  62. (A.K. Kingsbury and R.Y. Sharp) Asymptotic behaviour of certain sets of prime ideals, Proc. Amer. Math. Soc., 124 (1996), 1703-1711.
  63. (I.H. Denizler and R.Y. Sharp) Co-Cohen-Macaulay Artinian modules over commutative rings, Glasgow Math. J., 38 (1996), 359-366.
  64. (H. Petzl and R.Y. Sharp) Comparison of graded and ungraded Cousin complexes, Proc. Edinburgh Math. Soc., 41 (1998), 289-301.
  65. Linear growth of primary decompositions of integral closures, J. Algebra, 207 (1998), 276-284.
  66. Graded local cohomology and some applications, Commutative algebra, algebraic geometry and computational methods (Ed. D. Eisenbud), (Springer, Berlin, 1999), pp. 123-134.
  67. (A.K. Kingsbury and R.Y. Sharp) Asymptotic behaviour of integral closures of ideals, Communications in Algebra, 27 (1999), 5939-5949.
  68. Bass numbers in the graded case, a-invariant formulas, and an analogue of Faltings' Annihilator Theorem, J. Algebra, 222 (1999), 246-270.
  69. Injective modules and linear growth of primary decompositions, Proc. Amer. Math. Soc., 128 (2000), 717-722.
  70. (M.P. Brodmann, C. Rotthaus and R.Y. Sharp) On annihilators and associated primes of local cohomology modules, J. Pure and Applied Algebra, 153 (2000), 197-227.
  71. (M.H. Dogani Aghcheghloo, R. Enshaei, S. Goto and R.Y. Sharp) Comparison of multigraded and ungraded Cousin complexes, Proc. Edinburgh Math. Soc., 44 (2001), 365-378.
  72. (M.P. Brodmann, M. Katzman and R.Y. Sharp) Associated primes of graded components of local cohomology modules, Transactions Amer. Math. Soc., 354 (2002), 4261-4283.
  73. (M.P. Brodmann and R.Y. Sharp) On the dimension and multiplicity of local cohomology modules, Nagoya Math. J., 167 (2002), 217-233.
  74. (M. Katzman and R.Y. Sharp) Some properties of top graded local cohomology modules, J. Algebra, 259 (2003) 599-612.
  75. (M.P. Brodmann and R.Y. Sharp) Geometric domains with specified pseudo-dimensions, J. Pure and Applied Algebra, 182 (2003), 151-164.
  76. Convergence of sequences of sets of associated primes, Proc. Amer. Math. Soc., 131 (2003), 3009-3017.
  77. (R.Y. Sharp and N. Nossem) Ideals in a perfect closure, linear growth of primary decompositions, and tight closure, Transactions Amer. Math. Soc., 356 (2004), 3687-3720.

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