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On Rings Whose Strongly Prime Ideals Are Completely Prime

Chan Huh

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

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Chang Ik Lee

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

Corresponding author.

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, and

Yang Lee

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

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https://doi.org/10.1142/S1005386710000295Cited by:2 (Source: Crossref)

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.

The first author was supported for two years by Busan National University Research Grant. The second author was supported by the scholarship from Brain Korea (BK21). The third author was supported by the Korea Research Foundation Grant funded by the Korean Government (KRF-2008-521-C00003).

Keywords:

AMSC: 16N40, 16N99, 16U80

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