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  最后修改时间: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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作者单位
C. SELVARAJ Department of Mathematics, Periyar University, Salem-636011, Tamilnadu, India 
L. MADHUCHELVI Department of Mathematics, Sri Sarada College, Salem-636016, Tamilnadu, India 
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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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