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)

 

 

Monic polynomials and generating ideals efficiently


Author: Budh Nashier
Journal: Proc. Amer. Math. Soc. 95 (1985), 338-340
MSC: Primary 13C05; Secondary 13F20
MathSciNet review: 806066
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: If $ I$ is an ideal containing a monic polynomial in $ R[T]$ where $ R$ is a semilocal ring, then $ I$ and $ I/{I^2}$ require the same minimal number of generators. An ideal containing a monic polynomial in a polynomial ring need not possess any minimal set of generators having a monic as a part of it.


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

  • [1] Daniel Ferrand, Suite régulière et intersection complète, C. R. Acad. Sci. Paris Sér. A-B 264 (1967), A427–A428 (French). MR 0219546
  • [2] A. V. Geramita and C. Small, Introduction to homological methods in commutative rings, Queen's Papers in Pure and Applied Mathematics, Vol. 43 (2nd ed.), Kingston, Ontario, Canada, 1979.
  • [3] T. Y. Lam, Serre’s conjecture, Lecture Notes in Mathematics, Vol. 635, Springer-Verlag, Berlin-New York, 1978. MR 0485842
  • [4] S. Mandal, On efficient generation of ideals, Invent. Math. 75 (1984), no. 1, 59–67. MR 728138, 10.1007/BF01403089
  • [5] Wolmer V. Vasconcelos, Ideals generated by 𝑅-sequences, J. Algebra 6 (1967), 309–316. MR 0213345

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 13C05, 13F20

Retrieve articles in all journals with MSC: 13C05, 13F20


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0806066-0
Article copyright: © Copyright 1985 American Mathematical Society