Pseudo-Valuation ‏‎Near ‎ring‎ and Pseudo-Valuation N-group in Near Rings

Subject Areas : Statistics

TAHEREH  ROUDBARYLOR ¹ (Department of Mathematics‎, Kerman Branch‎, ‎Islamic Azad University‎, Kerman‎, ‎Iran)
MAHDIEH  SADEGHI GOUGHERI ² (‎Department of mathematics‎, ‎Kerman Branch‎, ‎Islamic Azad University‎, ‎Kerman‎, ‎Iran)

Received: 2018-09-08 Accepted : 2020-01-09 Published : 2020-07-01

Keywords: ایده ال اول قوی, N- زیرگروه اول, N - زیرگروه اول قوی, حلقه ی نزدیک شبه-ارزیاب, N-زیرگروه شبه-ارزیاب,

Abstract :

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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