algebra universalis

, Volume 6, Issue 1, pp 131–145 | Cite as

Abstract commutative ideal theory without chain condition

  • D. D. Anderson


Prime Ideal Commutative Ring Maximal Element Residuated Lattice Principal Ideal 
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  1. [1]
    D. D. Anderson,Multiplicative Lattices, Dissertation, University of Chicago, 1974.Google Scholar
  2. [2]
    —,A remark on the lattice of ideals of a Prüfer domain, Pacific J. Math.57 (1975), 323–324.MATHMathSciNetGoogle Scholar
  3. [3]
    —,Distributive Noether lattices Michigan Math. J.22 (1975), 109–115.MATHMathSciNetCrossRefGoogle Scholar
  4. [4]
    D. D. Anderson, andE. W. Johnson,Weak join principal element lattices, Algebra Universalis (to appear).Google Scholar
  5. [5]
    K. P. Bogart,Structure theorems for regular local Noether lattices, Michigan Math. J.15 (1968), 167–176.MATHMathSciNetCrossRefGoogle Scholar
  6. [6]
    —,Distributive local Noether lattices, Michigan Math. J.16 (1969), 215–223.MATHMathSciNetCrossRefGoogle Scholar
  7. [7]
    R. P. Dilworth,Abstract commutative ideal theory, Pacific J. Math.12 (1962), 481–498.MATHMathSciNetGoogle Scholar
  8. [8]
    R. Gilmer,Multiplicative Ideal Theory, Marcel Dekker, New York, 1972.MATHGoogle Scholar
  9. [9]
    M. F. Janowitz,Principal multiplicative lattices, Pacific J. Math.33 (1970), 653–656.MATHMathSciNetGoogle Scholar
  10. [10]
    E. W. Johnson,A-transforms and Hilbert functions in local lattices, Trans. Amer. Math. Soc.137 (1969), 125–139.MATHMathSciNetCrossRefGoogle Scholar
  11. [11]
    E. W. Johnson,Join principal element lattices, Proc. Amer. Math. Soc. (to appear).Google Scholar
  12. [12]
    —, andJ. P. Lediaev,Representable distributive Noether lattices, Pacific J. Math.28 (1969), 561–564.MATHMathSciNetGoogle Scholar
  13. [13]
    — and—Join principal elements in Noether lattices, Proc. Amer. Math. Soc.36 (1962), 73–78.MathSciNetCrossRefGoogle Scholar
  14. [14]
    P. J. McCarthy,Principal elements of lattices of ideals, Proc. Amer. Math. Soc.30 (1971), 43–45.MATHMathSciNetCrossRefGoogle Scholar
  15. [15]
    M. Ward,Residuated distributive lattices, Duke Math. J.6 (1940), 641–651.MATHMathSciNetCrossRefGoogle Scholar
  16. [16]
    — andR. P. Dilworth,Residuated lattices, Trans. Amer. Math. Soc.45 (1939), 335–354.MATHMathSciNetCrossRefGoogle Scholar
  17. [17]
    —, and—,The lattice theory of ova. Ann. of Math.40 (1939), 600–608.MATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Birkhäuser Verlag 1976

Authors and Affiliations

  • D. D. Anderson
    • 1
    • 2
  1. 1.University of IowaIowa CityUSA
  2. 2.Virginia Polytechnic Institute and State UniversityBlacksburgUSA

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