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Proceedings of the American Mathematical Society

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



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
MathSciNet review: 0498533
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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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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