Rocky Mountain Journal of Mathematics

Flat Epimorphisms and a Generalized Kaplansky Ideal Transform

Jay Shapiro

Full-text: Open access

Article information

Source
Rocky Mountain J. Math., Volume 38, Number 1 (2008), 267-289.

Dates
First available in Project Euclid: 25 March 2008

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1206459508

Digital Object Identifier
doi:10.1216/RMJ-2008-38-1-267

Mathematical Reviews number (MathSciNet)
MR2397035

Zentralblatt MATH identifier
1195.13009

Subjects
Primary: 13B30: Rings of fractions and localization [See also 16S85] 13B10: Morphisms
Secondary: 13A10 13C11: Injective and flat modules and ideals

Citation

Shapiro, Jay. Flat Epimorphisms and a Generalized Kaplansky Ideal Transform. Rocky Mountain J. Math. 38 (2008), no. 1, 267--289. doi:10.1216/RMJ-2008-38-1-267. https://projecteuclid.org/euclid.rmjm/1206459508


Export citation

References

  • J. Brewer, The ideal transform and overrings of an integral domain, Math Z. 107 (1968), 254-263.
  • J. Brewer and R. Gilmer, Integral domains whose overrrings are ideal transforms, Math. Nach. 51 (1971), 301-306.
  • J.L. Bueso, P. Jara and A Verschoren, Compatibility, stability, and sheaves, Marcel Dekker, New York, 1995.
  • M. Fontana, Kaplansky ideal transform: A survey, Lecture Notes Pure Appl. Math. 205, Marcel Dekker, New York, 1999.% 271--263
  • M. Fontana and N. Popescu, Universal property of the Kaplansky ideal trasnform and affineness of open subsets, J. Pure Appl. Algebra 173 (2002), 121-134.
  • S. Glaz, Commutative coherent rings, Lecture Notes Math. 1371, Springer-Verlag, Berlin, 1989.
  • J. Golan, Localization of noncommutative rings, Marcel Dekker, New York, 1975.
  • A. Grothendieck and J. Dieudonné, Eléments de Géométrie Algebrique I, Springer, Berlin, 1971.
  • J.R. Hedstrom, Domains of Krull type and ideal transforms, Math. Nach. 53 (1972), 101-118.
  • J.R. Hedstrom, $G$-Domains and property $(T)$, Math Nach. 56 (1973), 125-129.
  • J. Huckaba, Commutative rings with zero divisors, Marcel Dekker, New York, 1988.
  • D. Lazard, Epimorphismes plats, Séminaire Samuel 1967/69, Exposé 4, Paris, 1968.
  • E.L. Popescu, On a paper of Peter Schenzel, Rom. Math. Pures Appl. 40 (1995), 521-525.
  • B. Stenström, Rings of quotients, Springer-Verlag, New York, 1975.
  • B.R. Tennison, Sheaf theory, Cambridge University Press, Cambridge, 1975.