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

DOI：10.3770/j.issn:2095-2651.2012.01.003

 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

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.

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.