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Finitely generated powers of prime ideals

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 نشر من قبل Francois Couchot
 تاريخ النشر 2016
  مجال البحث
والبحث باللغة English
 تأليف Francois Couchot




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Let R be a commutative ring. If P is a maximal ideal of R whose a power is finitely generated then we prove that P is finitely generated if R is either locally coherent or arithmetical or a polynomial ring over a ring of global dimension $le$ 2. And if P is a prime ideal of R whose a power is finitely generated then we show that P is finitely generated if R is either a reduced coherent ring or a polynomial ring over a reduced arithmetical ring. These results extend a theorem of Roitman, published in 2001, on prime ideals of coherent integral domains.



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