On Rings Whose Strongly Prime Ideals Are Completely Prime-Reference-Cited by-同舟云学术

On Rings Whose Strongly Prime Ideals Are Completely Prime

Published:2010-06 Issue:02 Volume:17 Page:283-294
ISSN:1005-3867
Container-title:Algebra Colloquium
language:en
Short-container-title:Algebra Colloq.

Author:

Huh Chan¹,Lee Chang Ik¹,Lee Yang²

Affiliation:

1. Department of Mathematics, Pusan National University, Pusan 609-735, Korea

2. Department of Mathematics of Education, Pusan National University, Pusan 609-735, Korea

Abstract

Kaplansky introduced the concept of the K-rings, concerning the commutativity of rings. In this paper, we concentrate on a property of K-rings, introducing the concept of the strongly NI rings, which is stronger than NI-ness. We first examine the relations among the concepts concerned with K-rings and strongly NI rings, constructing necessary examples in the process. We also show that strong NI-ness is a hereditary radical property.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1005386710000295

Reference22 articles.

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2. G. F. Birkenmeier, H. E. Heatherly and E. K. Lee, Ring Theory (Granville, OH, 1992), Completely prime ideals and associated radicals, eds. S. K. Jain and S. T. Rizvi (World Scientific, Singapore-New Jersey-London-Hong Kong, 1993) pp. 102–129.

3. A connection between weak regularity and the simplicity of prime factor rings

4. An Introduction to Noncommutative Noetherian Rings;Goodearl K. R.,2004

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