Multi-ideal-adic completions of Noetherian rings
William Heinzer, Christel Rotthaus, and Sylvia Wiegand
Source: Michigan Math. J. Volume 57 (2008), 427-438.
Primary Subjects: 13B35, 13E05, 13F40
Secondary Subjects: 13H05, 13J10, 13J15
Full-text: Access denied (no subscription detected)
We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber.
If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.mmj/1220879416
Digital Object Identifier: doi:10.1307/mmj/1220879416
Mathematical Reviews number (MathSciNet):
MR2492460
Zentralblatt MATH identifier:
05604539
References
M. Atiyah and I. Macdonald, Introduction to commutative algebra, Addison-Wesley, London, ON, 1969.
Mathematical Reviews (MathSciNet):
MR242802
Zentralblatt MATH:
0175.03601
M. Brodmann and C. Rotthaus, Local domains with bad sets of formal prime divisors, J. Algebra 75 (1982) 386--394.
Mathematical Reviews (MathSciNet):
MR653898
Digital Object Identifier: doi:10.1016/0021-8693(82)90046-1
------, A peculiar unmixed domain, Proc. Amer. Math. Soc. 87 (1983), 596--600.
Mathematical Reviews (MathSciNet):
MR687624
Digital Object Identifier: doi:10.2307/2043342
JSTOR: links.jstor.org
W. Heinzer, C. Rotthaus, and S. Wiegand, Noetherian rings between a semilocal domain and its completion, J. Algebra 198 ( 1997), 627--655.
Mathematical Reviews (MathSciNet):
MR1489916
Digital Object Identifier: doi:10.1006/jabr.1997.7169
------, Building Noetherian and non-Noetherian integral domains using power series, Ideal theoretic methods in commutative algebra (D. D. Anderson, Ira Papick, eds.), Lecture Notes in Pure and Appl. Math., 220, pp. 251--264, Dekker, New York, 2001.
Mathematical Reviews (MathSciNet):
MR1836605
Zentralblatt MATH:
1008.13006
------, Integral closures of ideals in completions of regular local domains, Commutative algebra, Lect. Notes Pure Appl. Math., 244, pp. 141--150, Chapman & Hall/CRC, Boca Raton, FL, 2006.
R. Heitmann, A non-catenary, normal, local domain, Rocky Mountain J. Math. 12 (1982), 45--148.
Mathematical Reviews (MathSciNet):
MR649747
H. Matsumura, Commutative algebra, 2nd ed., Math. Lecture Note Ser., 56, Benjamin, Reading, MA, 1980.
Mathematical Reviews (MathSciNet):
MR266911
Zentralblatt MATH:
0211.06501
------, Commutative ring theory, 2nd ed., Cambridge Stud. Adv. Math., 8, Cambridge Univ. Press, Cambridge, 1989.
Mathematical Reviews (MathSciNet):
MR1011461
Zentralblatt MATH:
0666.13002
M. Nagata, Local rings, Interscience, New York, 1962.
Mathematical Reviews (MathSciNet):
MR155856
Zentralblatt MATH:
0123.03402
J. Nishimura, A few examples of local rings I, preprint.
------, A few examples of local rings II, preprint.
D. G. Northcott, Lessons on rings, modules and multiplicities, Cambridge Univ. Press, Cambridge, 1968.
Mathematical Reviews (MathSciNet):
MR231816
Zentralblatt MATH:
0159.33001
T. Ogoma, Non-catenary pseudo-geometric normal rings, Japan. J. Math. 6 (1980), 147--163.
------, Cohen--Macaulay factorial domain is not necessarily Gorenstein, Mem. Fac. Sci. Kochi Univ. Ser. A Math. 3 (1982), 65--74.
Mathematical Reviews (MathSciNet):
MR643928
M. Raynaud, Anneaux locaux Henseliens, Lecture Notes in Math., 169, Springer-Verlag, Berlin, 1970.
Mathematical Reviews (MathSciNet):
MR277519
C. Rotthaus, Universell Japanische ringe mit nicht offenem regulärem ort, Nagoya Math. J. 74 (1979), 123--135.
Mathematical Reviews (MathSciNet):
MR535964
Project Euclid: euclid.nmj/1118785800
------, Komplettierung semilokaler quasiausgezeichneter Ringe, Nagoya Math. J. 76 (1979), 173--180.
Mathematical Reviews (MathSciNet):
MR550860
Project Euclid: euclid.nmj/1118785940
H. Seydi, Anneaux henseliens et conditions de chaines, Bull. Soc. Math. France 98 (1970), 9--31.
Mathematical Reviews (MathSciNet):
MR262220
D. Weston, On descent in dimension two and non-split Gorenstein modules, J. Algebra 118 (1988), 263--275.
Mathematical Reviews (MathSciNet):
MR969672
Digital Object Identifier: doi:10.1016/0021-8693(88)90021-X
The Michigan Mathematical Journal