z⁰-Ideals and some special commutative rings

• Autorzy: Karim Samei
• Języki publikacji: EN

Abstrakty

EN

In a commutative ring R, an ideal I consisting entirely of zero divisors is called a torsion ideal, and an ideal is called a z⁰-ideal if I is torsion and for each a ∈ I the intersection of all minimal prime ideals containing a is contained in I. We prove that in large classes of rings, say R, the following results hold: every z-ideal is a z⁰-ideal if and only if every element of R is either a zero divisor or a unit, if and only if every maximal ideal in R (in general, every prime z-ideal) is a z⁰-ideal, if and only if every torsion z-ideal is a z⁰-ideal and if and only if the sum of any two torsion ideals is either a torsion ideal or R. We give a necessary and sufficient condition for every prime z⁰-ideal to be either minimal or maximal. We show that in a large class of rings, the sum of two z⁰-ideals is either a z⁰-ideal or R and we also give equivalent conditions for R to be a PP-ring or a Baer ring.

Kategorie tematyczne

• 54C40: Algebraic properties of function spaces
• 13A15: Ideals; multiplicative ideal theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2006
• Tom: 189
• Numer: 2
• Strony: 99-109

Daty

wydano

2006

Twórcy

autor

Karim Samei

• Department of Mathematics, Bu Ali Sina University, Hamedan, Iran
• Institute for Studies, in Theoretical Physics and Mathematics (IPM), Tehran, Iran

Identyfikatory

DOI

10.4064/fm189-2-1