On Weakly Primary Ideals

By Shahabaddin Ebrahimi Atani, F. Farzalipour. Georgian Mathematical Journal, 2005

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Abstract Weakly prime ideals in a commutative ring with non-zero identity have been introduced and studied in Anderson and Smith, Houston J. Math. 29: 831840, 2003. Here we study the weakly primary ideals of a commutative ring. We define a proper ideal 𝑃 of 𝑅 to be weakly primary if 0 𝑝𝑞 𝑃 implies 𝑝 𝑃 or 𝑞 Rad(𝑃), so every weakly prime ideal is weakly primary. Various properties of weakly primary ideals are considered. For example, we show that a weakly primary ideal 𝑃 that is not primary satisfies Rad(𝑃) Rad(0). Also, we show that an intersection of a family of weakly primary ideals that are not primary is weakly primary.

Subfields: Algebra and Number Theory

View Paper: https://www.semanticscholar.org/paper/cb23147762e87e1c5586f837afbb8d61ffaedaea

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In Algebra and Number Theory

1. Daniel D. Anderson
2. Malik Bataineh
3. Ayman Badawi

Citations in the corpus

• Generalizations of Prime Ideals (2008, background): “Weakly primary ideals are studied in Atani and Farzalipour (2005).”