Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

On the Noetherian-like rings of E. G. Evans


Authors: William Heinzer and Jack Ohm
Journal: Proc. Amer. Math. Soc. 34 (1972), 73-74
MSC: Primary 13E05
DOI: https://doi.org/10.1090/S0002-9939-1972-0294316-2
MathSciNet review: 0294316
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that if a commutative ring with identity R is nonnoetherian, then the polynomial ring in one indeterminate over R has an ideal with infinitely many maximal prime divisors (in the sense of Nagata).


References [Enhancements On Off] (What's this?)

  • [1] E. G. Evans, Zero divisors in noetherian-like rings, Trans. Amer. Math. Soc. 155 (1971), 505-512. MR 0272773 (42:7654)
  • [2] W. Heinzer and J. Ohm, Locally noetherian commutative rings, Trans. Amer. Math. Soc. 158 (1971), 273-284. MR 0280472 (43:6192)
  • [3] W. Krull, Über Laskersche Ringe, Rend. Circ. Mat. Palermo (2) 7 (1958), 155-166. MR 23 #A1664. MR 0124350 (23:A1664)
  • [4] D. Underwood, On some uniqueness questions in primary representations of ideals, J. Math. Kyoto Univ. 9 (1969), 69-94. MR 40 #134. MR 0246865 (40:134)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 13E05

Retrieve articles in all journals with MSC: 13E05


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0294316-2
Keywords: Noetherian ring, zero-divisor ring, maximal N-prime
Article copyright: © Copyright 1972 American Mathematical Society

American Mathematical Society