Pseudo-Valuation Near ring and Pseudo-Valuation N-group in Near Rings
In this paper, persents the definitions of strongly prime ideal, strongly prime N-subgroup, Pseudo-valuation near ring and Pseudo-valuation N-group. Some of their properties have also been proven by theorems. Then it is shown that, if N be near ring with quotient near-field K and P be a strongly prime ideal of near ring N, then is a strongly prime ideal of , for any multiplication subset S of N. In addition, they obtained the relation between strongly prime ideal and strongly prime N-group, and also between Pseudo-valuation near ring and Pseudo-valuation N-subgroup. It has also shown that if every N-subgroup be ideal of M and P be a strongly prime N-subgroup of M, then (P: M) is a strongly prime ideal of N. And in the end it is proved that if P and L of N-subgroups M and Psubset of L such that for any y in K ,y-1P subset of P , then L is a strongly prime N-subgroup of M if and only if L/p is a strongly prime N-subgroup of M/p .
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