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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
DOI: https://doi.org/10.1090/S0002-9939-1985-0806066-0
MathSciNet review: 806066
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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.


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