Well behaved prime t-ideals. (English) Zbl 0705.13001

Zafrullah, Muhammad

J. Pure Appl. Algebra 65, No. 2, 199-207 (1990).

In the integral domain \(D\), the fractional ideal \(A\) is a t-ideal if \(A=\cup (F^{-1})^{-1}\), over all finitely generated nonzero subideals of \(A\). Let \(P\) be an integral prime t-ideal of \(D\). This paper characterizes when \(PD_P\) is again a t-ideal. If \(P\) is also maximal with respect to being a t-ideal, and if \(PD_P\) is again a t-ideal, an example is given to show that there may be a prime t-ideal \(Q\leq P\) with \(QD_Q\) not a t-ideal. It is concluded that t-idealness is often lost upon localization.

Reviewer: Stephen McAdam (Austin)

MSC:

13A15	Ideals and multiplicative ideal theory in commutative rings
13B30	Rings of fractions and localization for commutative rings

Keywords:

t-ideal; localization

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