List of Articles strongly prime

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  1 - Pseudo-Valuation ‏‎Near ‎ring‎ and Pseudo-Valuation N-group in Near Rings
  TAHEREH ROUDBARYLOR MAHDIEH SADEGHI GOUGHERI
  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-f More

  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 . Manuscript profile
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  2 - Graded strongly prime submodules over graded commutative rings
  Farkhondeh Farzalipour Peyman Ghiasvand Masoomeh Hezarjaribi Dastaki
  10.30495/jnrm.2023.69642.2327
  Let G be a group with identity e, R a graded ring and M a graded R-module. ‎A‎ proper graded submodule ‎ N of ‎ M ‎is said ‎‎to ‎be‎ graded strongly ‎‎prime,‎ if we have ((N+Rx_g):_R⁡M)y_h⊆N, then x_g∈ N or y_h&i More

  Let G be a group with identity e, R a graded ring and M a graded R-module. ‎A‎ proper graded submodule ‎ N of ‎ M ‎is said ‎‎to ‎be‎ graded strongly ‎‎prime,‎ if we have ((N+Rx_g):_R⁡M)y_h⊆N, then x_g∈ N or y_h∈N ‎‎for all x_g,y_h∈h(M)‎‎‎‎‎. In this paper, we introduce the concept of graded strongly prime submodules as a generalization of graded prime submodules and we investigate some examples and basic properties of graded strongly prime submodules and state new results in this regard. In fact, in this article we show that the concept of graded strongly prime submodules is different from the concept of graded prime submodules. In continuing, we study the behavior of this structure module homomorphis, localization, quotient modules, Cartesian product. Finally, we state two kind of graded submodules of the amalgamation module along a graded ideal and investigate conditions under which they are graded strongly prime. Manuscript profile
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  3 - Some results on graded $S$-strongly prime submodules
  F. Farzalipour
  ‎Let $G$ be a group with identity $e$ and $R$ be a commutative $G$-graded ring with nonzero identity‎, ‎$S\subseteq h(R)$ a multiplicatively closed subset of $R$ and $M$ be a graded $R$-module‎. ‎A graded submodule $N$ of $M$ with $(N:_{R}M)\cap S=\emptyset$ is said to More

  ‎Let $G$ be a group with identity $e$ and $R$ be a commutative $G$-graded ring with nonzero identity‎, ‎$S\subseteq h(R)$ a multiplicatively closed subset of $R$ and $M$ be a graded $R$-module‎. ‎A graded submodule $N$ of $M$ with $(N:_{R}M)\cap S=\emptyset$ is said to be graded $S$-strongly prime if there exists $s\in S$ such that whenever $((N+Rx_{g}):_{R}M)y_{h}\subseteq N$‎, ‎then $sx_{g}\in N$ or $sy_{h}\in N$ for all $x_{g},y_{h}\in h(M)$‎. ‎The aim of this paper is to introduce and investigate some basic properties of the notion of graded $S$-strongly prime submodules‎, ‎especially in graded multiplication modules‎. ‎Moreover‎, ‎we investigate the behaviour of this structure under graded module homomorphisms‎, ‎localizations of graded modules‎, ‎quotient graded modules‎, ‎Cartesian product‎. Manuscript profile