2006Fundamenta MathematicaeOpen access

z0-Ideals and some special commutative rings

Karim Samei

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Abstract

In a commutative ring $R$, an ideal $I$ consisting entirely of zero divisors is called a torsion ideal, and an ideal is called a $z^0$-ideal if $I$ is torsion and for each $a \in I$ the intersection of all minimal prime ideals containing $a$ is contained

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In a commutative ring $R$, an ideal $I$ consisting entirely of zero divisors is called a torsion ideal, and an ideal is called a $z^0$-ideal if $I$ is torsion and for each $a \in I$ the intersection of all minimal prime ideals containing $a$ is contained

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Available abstract

In a commutative ring $R$, an ideal $I$ consisting entirely of zero divisors is called a torsion ideal, and an ideal is called a $z^0$-ideal if $I$ is torsion and for each $a \in I$ the intersection of all minimal prime ideals containing $a$ is contained

Key concepts: Mathematics, Minimal ideal, Commutative ring, Radical of an ideal, Associated prime, Torsion (gastropod), Prime ideal, Ideal (ethics)

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