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2011•Journal of Advanced Social ResearchRequires access

S2 Ideals In Commutative Rings

Sarab A. Al-Taha

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Abstract

Let R be a commutative ring with identity, let a be a nonzero element in R. In (Al-Taha, 2011) we give the definition of s1 ideal and we study some of its properties, while this paper deals with a new definition for the principal ideal I= of the ring R that we call s2 ideal, we give some results about s2 ideals also we give the relation between s2 ideals and s1 ideals. We prove the following result among others the ideal I = is s2 ideal of R if, and only if I= is s2 ideal of R[x1, x2,…,xn].

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What this paper is about

Let R be a commutative ring with identity, let a be a nonzero element in R. In (Al-Taha, 2011) we give the definition of s1 ideal and we study some of its properties, while this paper deals with a new definition for the principal ideal I= of the ring R that we call s2 ideal, we give some results about s2 ideals also we give the relation between s2 ideals and s1 ideals. We prove the following result among others the ideal I = is s2 ideal of R if, and only if I= is s2 ideal of R[x1, x2,…,xn].

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Available abstract

Let R be a commutative ring with identity, let a be a nonzero element in R. In (Al-Taha, 2011) we give the definition of s1 ideal and we study some of its properties, while this paper deals with a new definition for the principal ideal I= of the ring R that we call s2 ideal, we give some results about s2 ideals also we give the relation between s2 ideals and s1 ideals. We prove the following result among others the ideal I = is s2 ideal of R if, and only if I= is s2 ideal of R[x1, x2,…,xn].

Key concepts: Ideal (ethics), Principal ideal, Primary ideal, Mathematics, Commutative ring, Radical of an ideal, Minimal ideal, Maximal ideal

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