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)

 
 

 

Unibranched prime ideals and going down in PI rings


Author: Phillip Lestmann
Journal: Proc. Amer. Math. Soc. 82 (1981), 191-195
MSC: Primary 16A33; Secondary 16A38
DOI: https://doi.org/10.1090/S0002-9939-1981-0609649-2
MathSciNet review: 609649
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The purpose of this paper is to answer the question of whether going down is equivalent to unibranchedness of prime ideals in integral extensions of prime $ {\text{PI}}$ rings. We show by example that, in general, the answer is no; and we find an additional condition which, together with going down, implies prime ideals of $ {\text{ht}} > 1$ are unibranched.


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

  • [1] S. A. Amitsur and L. Small, Prime $ {\text{PI}}$-rings, Bull. Amer. Math. Soc. 83 (1977), 249-251. MR 0435134 (55:8095)
  • [2] V. A. Jategaonkar, Principal ideal theorem for Noetherian $ {\text{P}}.{\text{I}}.$ rings, J. Algebra 35 (1975), 17-22. MR 0371944 (51:8161)
  • [3] Phillip Lestmann, Going down and the spec map in $ {\text{PI}}$ rings, Comm. Algebra 6(16) (1978), 1667-1691. MR 508243 (80a:16032)
  • [4] Stephen McAdam, Going down, Duke Math. J. 39 (1972), 633-636. MR 0311658 (47:220)
  • [5] Neal H. McCoy, A note on finite unions of ideals and subgroups, Proc. Amer. Math. Soc. 8 (1957), 633-637. MR 0086803 (19:246b)
  • [6] Claudio Procesi, Rings with polynomial identities, Dekker, New York, 1973. MR 0366968 (51:3214)
  • [7] William Schelter, Integral extensions of rings satisfying a polynomial identity, J. Algebra 40 (1976), 245-257. MR 0417238 (54:5295)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 16A33, 16A38

Retrieve articles in all journals with MSC: 16A33, 16A38


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1981-0609649-2
Keywords: Integral extension, integral closure, going down, prime ideal, $ {\text{PI}}$ ring, Noetherian, unibranched
Article copyright: © Copyright 1981 American Mathematical Society

American Mathematical Society