| C. SELVARAJ,L. MADHUCHELVI.Characterization of $2$-Primal Near-Rings[J].数学研究及应用,2012,32(1):19~25 |
| Characterization of $2$-Primal Near-Rings |
| Characterization of $2$-Primal Near-Rings |
| 投稿时间：2010-03-12 修订日期：2010-04-27 |
| DOI：10.3770/j.issn:2095-2651.2012.01.003 |
| 中文关键词: 2-primal completely prime completely semiprime. |
| 英文关键词:2-primal completely prime completely semiprime. |
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| 中文摘要: |
| In 1999, Kim and Kwak asked one question that ``Is a ring $R$ $2$-primal if $O_{P}\subseteq P$ for each $P\in m{\rm Spec}(R)?"$. In this paper, we prove that if $O_{P}$ has the IFP for each $P \in m{\rm Spec}(N)$, then $O_{P} \subseteq P$ for each $P \in m{\rm Spec}(N)$ if and only if $N$ is a $2$-primal near-ring and also we give characterization of 2-primal near-rings by using its minimal $0$-prime ideals. |
| 英文摘要: |
| In 1999, Kim and Kwak asked one question that ``Is a ring $R$ $2$-primal if $O_{P}\subseteq P$ for each $P\in m{\rm Spec}(R)?"$. In this paper, we prove that if $O_{P}$ has the IFP for each $P \in m{\rm Spec}(N)$, then $O_{P} \subseteq P$ for each $P \in m{\rm Spec}(N)$ if and only if $N$ is a $2$-primal near-ring and also we give characterization of 2-primal near-rings by using its minimal $0$-prime ideals. |
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