The Laskerian property, power series rings and Noetherian spectra
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Let R be a commutative ring with identity. An ideal Q of R is primary if each zero divisor of the ring R/ Q is nilpotent, and Q is strongly primary if Q is primary and contains a power of its radical. In the terminology of Bourbaki [B, Ch. IV, pp. 295, 298], the ring R is Laskerian if each ideal of R is a finite intersection of primary ideals, and R is strongly Laskerian if each ideal of R is a finite intersection of strongly primary ideals. It is well known that
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