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2013•Communications in AlgebraRequires access

Strongly 0-Dimensional Rings

C. Jayaram, Kürşat Hakan Oral, Ünsal Teki̇̀r

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Abstract

A commutative ring R with identity is called a strongly 0-dimensional ring if whenever a prime ideal P of R, contains the intersection of any family of ideals, then P contains one of the ideals of the family. In this article, we establish several equivalent conditions for a commutative ring R with identity to be a strongly 0-dimensional ring. We also characterize Artinian rings in terms of strongly 0-dimensional rings.

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What this paper is about

A commutative ring R with identity is called a strongly 0-dimensional ring if whenever a prime ideal P of R, contains the intersection of any family of ideals, then P contains one of the ideals of the family. In this article, we establish several equivalent conditions for a commutative ring R with identity to be a strongly 0-dimensional ring. We also characterize Artinian rings in terms of strongly 0-dimensional rings.

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Available abstract

A commutative ring R with identity is called a strongly 0-dimensional ring if whenever a prime ideal P of R, contains the intersection of any family of ideals, then P contains one of the ideals of the family. In this article, we establish several equivalent conditions for a commutative ring R with identity to be a strongly 0-dimensional ring. We also characterize Artinian rings in terms of strongly 0-dimensional rings.

Key concepts: Mathematics, Commutative ring, Noncommutative ring, Principal ideal ring, Artinian ring, Reduced ring, Pure mathematics, Simple ring

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