Volume 5, Issue 1 (May 2010)                   IJMSI 2010, 5(1): 19-26 | Back to browse issues page

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Jahani-Nezhad R. The Dual of a Strongly Prime Ideal. IJMSI 2010; 5 (1) :19-26
URL: http://ijmsi.ir/article-1-107-en.html

Let R be a commutative integral domain with quotient field K and let P be a nonzero strongly prime ideal of R. We give several characterizations of such ideals. It is shown that (P : P) is a valuation domain with the unique maximal ideal P. We also study when P^{&minus1} is a ring. In fact, it is proved that P^{&minus1} = (P : P) if and only if P is not invertible. Furthermore, if P is invertible, then R = (P : P) and P is a principal ideal of R.

Type of Study: Research paper | Subject: General

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