UCR

Department of Mathematics



David Rush Publications


Technical Publications


Journal Articles

1. Ohm, J., Rush, D. 1971. The Finiteness of I when R(X)/I is Flat. Bulletin of the American Mathematical Society. p.793-796. (Refereed)  

2. Cox, Jr, S., Rush, D. 1972. Endomorphisms of Finite Rank Flat Modules. Duke Mathematical Journal. p.323-326. (Refereed)  

3. Ohm, J., Rush, D. 1972. The Finiteness of I when R(X)/I is flat. American Mathematical Society. p.377-408. (Refereed)

4. Ohm, J., Rush, D. 1972. Content Modules and Algebras. Math. Scand. p.49-68. (Refereed)  

5. Rush, D. 1974. The G-function of MacRae. The Canadian Journal of Mathematics. p.854-865. (Refereed)  

6. Cox, Jr, S., Rush, D. 1974. Finiteness in Flat Modules and Algebras. Journal of Algebra. p.44-50. (Refereed)  

7. Rush, D. 1976. Remarks on Flat Modules. Michigan Mathematical Journal. p.193-201. (Refereed)  

8. Rush, D. 1977. Some Applications of Griffith's Basic Submodules. Journal of Pure and Applied Algebra. p.41-44. (Refereed)  

9. Ratliff, Jr., L.J., Rush, D. 1977. Notes on Ideal Covers and Associated Primes. Pacific Journal of Mathematics. p.169-191. (Refereed)  

10. McAdam, S., Rush, D. 1978. Schreier Rings. Bull. London Math. Soc. p.77-80. (Refereed)  

11. Rush, D. 1978. Content Algebras. Canad. Math. Bull. p.329-334. (Refereed)  

12. Ratliff, Jr., L.J., Rush, D. 1978. Two Notes on Reductions of Ideals. Indiana University Mathematics Journal. p.929-934. (Refereed)  

13. Rush, D. 1979. Pic(R) and the R-Flatness of R(X)/I. Journal of Pure and Applied Algebra. p.307-310. (Refereed)  

14. Rush, D. 1980. Big Cohen-Macaulay Modules. Illinois Journal of Mathematics. p.606-611. (Refereed)  

15. Rush, D. 1980. Seminormality. Journal of Algebra. p.377-384. (Refereed)  

16. Rush, D. 1982. Picard Groups in Abelian Group Rings. Journal of Pure and Applied Algebra. p.101-114. (Refereed)  

17. Rush, D. 1983. Rings which Resemble Rings of Entire Functions. Glasgow Math. J. p.7-16. (Refereed)  

18. Rush, D. 1983. The equation Xk + Yk = Zk in Commuting Rational Matrices. Canad. Math. Bull. p.406-409. (Refereed)  

19. Rush, D. 1983. An arithmetic characterization of algebraic number fields with a given class group. Math. Proc. Camb. Phil. Soc. p.23-28. (Refereed) 

20. Iroz, J., Rush, D. 1984. Associated Prime Ideals in Non-Noetherian Rings. Canad. J. Math. p.344-360. (Refereed) 

21. Rush, D. 1985. Generating Ideals in Rings of Integer-Valued Polynomials. Journal of Algebra. p.389-394. (Refereed)  

22. Rush, D. 1988. Reflexive D-Rings. Journal of Algebra. p.81-88. (Refereed)  

23. Ratliff, Jr., L.J., Rush, D. 1988. Note on I-Good Filtrations and Noetherian Rees Rings. Communications in Algebra. p.955-975. (Refereed)  

24. Rush, D. 1988. Integrally Closed Torsionless Rings. Canad. Math. Bull. p.215-216. (Refereed)  

25. Rush, D. 1988. Torsionfree Modules Over One-Dimensional Noetherian Rings. Journal of Pure and Applied Algebra. p.133-146. (Refereed)  

26. Mirbagheri, A., Ratliff, Jr., L.J., Rush, D. 1989. Superficial Sets of Elements for Sets of Ideals. Communications in Algebra. p.3087-3108. (Refereed) 

27. Bishop, W., Petro, J.W., Ratliff, Jr., L.J., Rush, D. 1989. Note on Noetherian Filtrations. Communications in Algebra. p.471-485. (Refereed)  

28. Rush, D. 1991. Rings with two-generated ideals. Journal of Pure and Applied Algebra. p.257-275. (Refereed)  

29. Ratliff, Jr., L.J., Rush, D. 1991. Note on Divisorial Sets of Elements for Sets of Ideals. Communications in Algebra. p.223-248. (Refereed) 

30. Okon, J.S., Rush, D., Vicknair, P. 1992. Commutative Semigroup Rings with Two-Generated Ideals. J. London Math. Soc. p.417-432. (Refereed)  

31. Rush, D. 1992. Asymptotic Primes and Integral Closure in Modules. Quarterly J. Math. Oxford. p.477-499. (Refereed)  

32. Rush, D. 1992. Artin Rings with Two-Generated Ideals. Canad. Math. Bull. p.133-135. (Refereed)  

33. Ratliff, Jr, L., Rush, D. 1993. Δ-Reductions of Modules. Communications in Algebra. p.2667-2685. (Refereed)  

34. Rush, D. 1995. Two-Generated Ideals and Representations of Abelian Groups over Valuation Rings. Journal of Algebra. p.77-101. (Refereed)  

35. Okon, J.S., Rush, D., Vicknair, P. 1996. Two-generated ideals in non-Noetherian semigroup rings. Journal of Pure and Applied Algebra. p.255-276. (Refereed)  

36. Okon, J.S., Rush, D., Vicknair, P. 1997. Numbers of Generators of Ideals in Zero-Dimensional Group Rings. Communications in Algebra. p.803-831. (Refereed)  

37. Rush, D. 1997. Generating Ideals Up to Radical in Noetherian Polynomial Rings. Communications in Algebra. p.2169-2191. (Refereed)  

38. Rush, D. 1998. The conditions Int(R)_ (Rs) = Int(R)s for integer-valued polynomials. Journal of Pure and Applied Algebra. p.287-303. (Refereed)  

39. Rush, D. 1999. Generating Ideals in Rings of Integer-Valued Polynomials. Canad. Math. Bull. p.231-236. (Refereed)  

40. Ratliff, Jr, L., Rush, D. 1999. Triangular powers of integers from determinants of binomial coefficient matrices. J. Linear Alg. and Applications. p.125-142. (Refereed)  

41. Ratliff, Jr, L., Rush, D. 1999. A Bracket Power Characterization of Analytic Spread One Ideals. Transactions of the American Mathematical Society. p.1647-1674. (Refereed, Electronic)  

42. Rush, D. 2000. The Dedekind-Mertens Lemma and the Contents of Polynomials. Proceedings of the American Mathematical Society. p.2879-2884. (Refereed, Electronic)  

43. Okon, J., Rush, D. 2000. Numbers of Generators of Ideals in a Group Ring of an Elementary Abelian p-Group. Journal of Algebra. p.1-22. (Refereed)  

44. Okon, J., Rush, D., Vicknair, J. Paul 2000. Numbers of Generators of Ideals in a Group Ring of an Elementary Abelian p-Group. Journal of Algebra. p.1-22. (Refereed)  

45. Rush, D. 2001. Bezout domains with stable range 1. Journal of Pure and Applied Algebra. p.309-324. (Refereed)  

46. Rush, D., Wallace, L. 2002. Noetherian Maximal Spectrum and Coprimely Packed Localizations of Polynomial Rings. Houston Journal of Mathematics. p.437-448. (Refereed)  

47. Heinzer, W., Ratliff, Jr, L., Rush, D. 2002. Strongly irreducible ideals of a commutative ring. Journal of Pure and Applied Algebra. p.267-275. (Refereed)  

48. Ratliff, Jr., L.J., Rush, D. 2002. Asymptotic Primes of Delta Closures of Ideals. Communications in Algebra. p.1513-1531. (Refereed)  

49. Heinzer, W., Ratliff, Jr, L., Rush, D. 2002. Basically Full Ideals in Local Rings. Journal of Algebra. p.371-396. (Refereed)  

50. Okon, J., Rush, D. 2002. Generating Ideals in Commutative Artinian Group Rings and a Generalized Pascal's Triangle. Communications in Algebra. p.5595-5607. (Refereed)  

51. Heinzer, W., Li, A., Ratliff, Jr, L., Rush, D. 2002. Monoidal Extensions of a Cohen-Macaulay Unique Factorization Domain. Transactions of the American Mathematical Society. p.1811-1835. (Refereed, Electronic)  

52. Rush, D. 2003. Noetherian properties in monoid rings. Journal of Pure and Applied Algebra. p.259-278. (Refereed)  

53. Ratliff, Jr, L., Rush, D. 2003. Two notes on homogeneous prime ideals in graded Noetherian rings. Journal of Algebra. p.211-230. (Refereed)  

54. Rush, D. 2003. Quadratic Polynomials, Factorization in Integral Domains and Schreier Domains from Pullbacks. Mathematika. p.103-112. (Refereed)  

55. Ciuperca, C., Heinzer, W., Ratliff, Jr, L., Rush, D. 2004. Projectively equivalent ideals and Rees valuations. Journal of Algebra. p.140-156. (Refereed)  

56. Ratliff, Jr, L., Rush, D., Shah, K. 2004. Note on Cyclotomic Polynomials and Prime Ideals. Communications in Algebra. p.333-343. (Refereed)

57. Ratliff, Jr, L., Rush, D. 2004. Symmetric Reductions. Communications in Algebra. p.3189-3213. (Refereed)

58. Brookfield, G., Rush, D. 2005. When graded domains are Schreier or pre-Schreir. Journal of Pure and Applied Algebra. p.225-230. (Refereed)  

59. Culhan, D., Rush, D. 2005. Primal decomposition in rings, modules and lattice modules. Algebra Universalis. p.167-184. (Refereed)  

60. Okon, J., Rush, D., Wallace, L. 2005. A Mori-Nagata Theorem for Lattices and Graded Rings. Houston Journal of Mathematics. p.973-997. (Refereed)

61. Ciuperca, C., Heinzer, W., Ratliff, Jr, L., Rush, D. 2006. Projectively full ideals in Noetherian rings. Journal of Algebra. p.73-93. (Refereed)  

62. Ratliff, Jr, L., Rush, D., Shah, K. 2006. Power integral bases for Selmer-like number fields. Journal of Number Theory. p.90-113. (Refereed)  

(In Press)

1. Ciuperca, C., Heinzer, W., Ratliff, Jr, L., Rush, D. Projectively full ideals in Noetherian rings (II). Journal of Algebra. (Accepted 01/18/2005. 29 manuscript pages.) (Refereed)

2. Okon, J., Rush, D., Wallace, L. A Mori-Nagata Type Theorem for Seminormal Mori Lattices. Houston Journal of Mathematics. (Accepted 08/26/2005. 19 manuscript pages.) (Refereed)

3. Brookfield, G., Rush, D. Convex Polytopes and Factorization Properties in Generalized Power Series Domains. Rocky Mountain J. of Math. (Accepted 04/18/2006. 10 manuscript pages.) (Refereed)  

4. Rush, D. Rees valuations and asymptotic primes of rational powers in Noetherian rings and lattices. Journal of Algebra. (Accepted 08/30/2006. 35 manuscript pages.) (Refereed)

 


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