Characterization of $2$-Primal Near-Rings |
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Authors: | C SELVARAJ and L MADHUCHELVI |
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Affiliation: | Department of Mathematics, Periyar University, Salem-636011, Tamilnadu, India;Department of Mathematics, Sri Sarada College, Salem-636016, Tamilnadu, India |
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Abstract: | 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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Keywords: | 2-primal completely prime completely semiprime |
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