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Proceedings of the American Mathematical Society

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

 

 

Symbolic powers of prime ideals and their topology


Author: Peter Schenzel
Journal: Proc. Amer. Math. Soc. 93 (1985), 15-20
MSC: Primary 13C15; Secondary 13A17, 13H10, 13J99
DOI: https://doi.org/10.1090/S0002-9939-1985-0766518-9
MathSciNet review: 766518
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Abstract: For a prime ideal $ P$ of a commutative Noetherian ring $ R$ a necessary and sufficient condition is given to determine when the $ P$-adic topology is equivalent, resp. linearly equivalent, to the $ P$-symbolic topology. The last means that the symbolic Rees ring is a finitely generated module over the ordinary Rees ring of $ P$. Then it is considered when the integral closure of all the powers of $ P$ are primary.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1985-0766518-9
Keywords: Prime ideal, symbolic power, asymptotic prime divisors, integral closure, Rees ring, form ring
Article copyright: © Copyright 1985 American Mathematical Society