Prime elements and prime sequences in polynomial rings

Author:
Edward D. Davis

Journal:
Proc. Amer. Math. Soc. **72** (1978), 33-38

MSC:
Primary 13F20; Secondary 14M10

DOI:
https://doi.org/10.1090/S0002-9939-1978-0498533-3

MathSciNet review:
0498533

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Abstract | References | Similar Articles | Additional Information

Abstract: The central question of this note concerns the existence of prime elements in polynomial rings. In it are established for polynomial rings over arbitrary noetherian rings--insofar as is generally possible--certain results concerning bases for maximal ideals, well known for polynomial rings over fields and principal ideal domains. These results may be interpreted geometrically as theorems about normal (and especially smooth) closed points on ruled schemes.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1978-0498533-3

Keywords:
Polynomial ring,
maximal ideal,
prime element,
prime sequence,
complete intersection,
Gauss' Lemma,
ruled affine scheme,
normal point,
smooth point

Article copyright:
© Copyright 1978
American Mathematical Society