Pacific Journal of Mathematics

Uniform dimensions and subdirect products.

John Dauns

Article information

Source
Pacific J. Math., Volume 126, Number 1 (1987), 1-19.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102699900

Mathematical Reviews number (MathSciNet)
MR868605

Zentralblatt MATH identifier
0597.16020

Subjects
Primary: 16A52
Secondary: 16A34

Citation

Dauns, John. Uniform dimensions and subdirect products. Pacific J. Math. 126 (1987), no. 1, 1--19. https://projecteuclid.org/euclid.pjm/1102699900


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References

  • [AF] F. Anderson, and K. Fuller, Rings and Categories of Modules, GraduateTexts in Math. 13, Springer (1973), New York.
  • [B] R. Bumby, Modules whichare isomorphicto submodulesof each other,Archiv. Math., XVI (1965), 184-185.
  • [C] A. Cailleau, One caracterisation des modules-injectives, C. R. Acad. Sci. Paris, 269 (1969), 997-999.
  • [CR] A. Cailleau and G. Renault, Etude des modules -quasi'injectifs, C. R. Acad. Sci. Paris, 270 (1970), 1391-1394.
  • [CF] S. Chase and C. Faith, Quotient rings and direct products of full linearrings, Math. Z., 88 (1965), 250-264.
  • [CJ] P. Crawley and B. Jonsson, Refinementsfor infinite direct decompositionsof algebraicsystems, Pacific J. Math., 14 (1964), 797-855.
  • [Dl] J. Dauns, Simple modulesand centralizers, T.A.M.S., 166 (1972), 457-477.
  • [D2] J. Dauns, Prime modules,J. Reine Angew. Math.,298 (1978), 156-181.
  • [D3] J. Dauns, Prime modulesand one sided ideals,Algebra Proceedings III, University of Oklahoma, 1979, Marcel Dekker (1979), New York, pp. 41-83.
  • [D4] J. Dauns, Uniformmodulesand complements,Houston J. Math.,6 (1980), 31-40.
  • [D5] J. Dauns, Sums of UniformModules, Advances in Noncommutatie RingTheory, Proceedings, Pittsburgh, 1981, Lecture Notes in Math. 951, Springer (1982), pp. 68-87.
  • [F] C. Faith, InjectiveModulesand Injective QuotientRings, Marcel Dekker (1982), New York.
  • [FW] C. Faith and E. A. Walker, Direct sum representations of injective modules,J. Algebra, 5 (1967), 203-221.
  • [FU] C. Faith and Y. Utumi, Quasi-injective modules and their endomorphism rings, Arch. Math., 15 (1964), 166-174.
  • [Ful] L. Fuchs, On subdirectunions. I, Acta Scient. Math.,Ill (1952), 103-120.
  • [Fu2] L. Fuchs, Infinite Abelian Groups, Vol. I, II,Academic Press (1970), New York.
  • [G] K. R. Goodearl, Ring Theory, Marcel Dekker, New York, 1976.
  • [GB] K. R. Goodearl and A. K. Boyle, Dimension Theoryfor Nonsingular Injective Modules, A.M.S. Memoir No. 177, Providence, R.I. 1976.
  • [GZ-H] K. R. Goodearl and B. Zimmermann-Huisgen, Boundedness of directproducts of torsionmodules, to appear.
  • [GoR] R. Gordon, Krull Dimension, A.M.S. Memoir No. 133, Providence, R.L, 1973.
  • [HJ] K. Hrbacek and T. Jech, Introduction to Set Theory, Marcel Dekker, Inc., Monographs in Pure and Applied Math. (1978), New York.
  • [J] J. Jans, Rings and Homology,Holt, Rinehart and Winston, New York, 1964.
  • [Kl] K. Koh, On some characteristic properties of self injectie rings, P.A.M.S., 19 (1968), 209-213.
  • [K2] K. Koh, Quasi-Simple Modules, Lectures on Rings and Modules, Lecture Notes in Math. 246, Springer (1972), New York.
  • [L] J. Lambek, Lectureson Rings and Modules, Chelsea Publ. Co.,New York, 1976.
  • [Le] A. Levy, Basic Set Theory, Perspectives in Math. Logic, Springer (1979).
  • [Lev] A. Levy, Unique subdirect sums of prime rings, Trans. Amer. Math. So, 106 (1963), 64-76.
  • [Lo] F. Loonstra, Essential submodules and essential subdirect products, Symposia Math., XXIII (1970), 85-105.
  • [M] E. Math's, Injectie modules over Noetherian rings, Pacific J. Math., 8 (1958), 511-528.
  • [MR] B. Mller and S. T. Rizvi, On the decompositionof continuousmodules, Canad. Math. Bull., 25 (1982), 296-301.
  • [SV] D. Sharpe and P. Vamos, Injectie Modules, Cambridge University Press, Cambr. Tracts in Math, and Math. Phys., 62 (1972).
  • [SI] B. Stenstrm, Puresubmodules, Arkiv for Mat, 7 (1967), 171-195.
  • [S2] B. Stenstrm, Direct sum decomposition in Grothendieckcategories,Arkiv for Mat., 7 (1968), 427-432.
  • [S3] B. Stenstrm, Rings of Quotients, Comprehensive Studies in Math. 217, Springer (1975), New York.
  • [St] H. Storrer, On Goldman's Primary Decomposition,Lecture Notes in Math. No. 246, Springer (1972), New York.
  • [Tl] M. Teply, Torsion free injectiemodules,Pacific J. Math., 28 (1969), 441-453.
  • [T2] M. Teply, Some aspects of Goldie's torsion theory, Pacific J. Math., 29 (1969), 447-459.
  • [W] R. B. Warfield, Decompositions of injectiemodules, Pacific J. Math., 31 (1969), 236-276.
  • [Z-H] B. Zimmermann-Huisgen, Direct products of torsion modules, Arch, der Math., 38 (1982), 426-431.
  • [Z-HZ] B. Zimmermann-Huisgen and W. Zimmerman, Classes of modules with the exchangeproperty, to appear.