• Journal of the Chungcheong Mathematical Society
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• v.16 no.2
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• pp.59-73
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• 2003

Throughout this paper, we denote that R is a near-ring and G an R-group. We initiate the study of R-substructures of G, representations of R on G, monogenic R-groups, faithful R-groups and faithful D.G. representations of near-rings. Next, we investigate some properties of monogenic near-ring groups, faithful monogenic near-ring groups, monogenic and faithful D.G. representations in near-rings.

• Journal of applied mathematics & informatics
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• v.26 no.1_2
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• pp.401-406
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• 2008

In this paper, we will introduce the noetherian quotients in R-groups, and then investigate the related substructures of the near-ring R and G and the R-group G. Also, applying the annihilator concept in R-groups and d.g. near-rings, we will survey some properties of the substructures of R and G in monogenic Rgroups, and show that R becomes a ring for faithful monogenic R-groups with some condition.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.2
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• pp.183-190
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• 2007

In this paper, we will introduce the noetherian quotients in R-groups, and then investigate the related substructures of the near-ring R and G and the R-group G. Also, applying the annihilator concept in R-groups and d.g. near-rings, we will survey some properties of the substructures of R and G in monogenic R-groups and faithful R-groups.

• Kyungpook Mathematical Journal
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• v.46 no.4
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• pp.603-613
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• 2006

Near-rings considered are right near-rings and R is a near-ring. $J_0^r(R)$, the right Jacobson radical of R of type-0, was introduced and studied by the present authors. In this paper $J_1^r(R)$ and $J_2^r(R)$, the right Jacobson radicals of R of type-1 and type-2 are introduced. It is proved that both $J_1^r$ and $J_2^r$ are radicals for near-rings and $J_0^r(R){\subseteq}J_1^r(R){\subseteq}J_2^r(R)$. Unlike the left Jacobson radical classes, the right Jacobson radical class of type-2 contains $M_0(G)$ for many of the finite groups G. Depending on the structure of G, $M_0(G)$ belongs to different right Jacobson radical classes of near-rings. Also unlike left Jacobson-type radicals, the constant part of R is contained in every right 1-modular (2-modular) right ideal of R. For any family of near-rings $R_i$, $i{\in}I$, $J_{\nu}^r({\oplus}_{i{\in}I}R_i)={\oplus}_{i{\in}I}J_{\nu}^r(R_i)$, ${\nu}{\in}\{1,2\}$. Moreover, under certain conditions, for an invariant subnear-ring S of a d.g. near-ring R it is shown that $J_2^r(S)=S{\cap}J_2^r(R)$.

• The Pure and Applied Mathematics
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• v.18 no.4
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• pp.305-312
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• 2011

In this paper, we denote that R is a near-ring and G an R-group. We initiate the study of the substructures of R and G. Next, we investigate some properties of R-groups, d.g. near-rings and monogenic (R, S)-groups.

• Journal of applied mathematics & informatics
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• v.40 no.5_6
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• pp.915-923
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• 2022

The purpose of the present paper is to obtain commutativity of prime Γ-near-ring N with generalized derivations F and G with associated derivations d and h respectively satisfying one of the following conditions:(i) G([x, y]α = ±f(y)α(xoy)βγg(y), (ii) F(x)βG(y) = G(y)βF(x), for all x, y ∈ N, β ∈ Γ (iii) F(u)βG(v) = G(v)βF(u), for all u ∈ U, v ∈ V, β ∈ Γ,(iv) if 0 ≠ F(a) ∈ Z(N) for some a ∈ V such that F(x)αG(y) = G(y)αF(x) for all x ∈ V and y ∈ U, α ∈ Γ.

• East Asian mathematical journal
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• v.25 no.2
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• pp.171-177
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• 2009

Throughout this paper, we denote that R is a near-ring and G an R-group. We initiate a study of R-substructures of G, monogenic R-groups, faithful R-groups and faithful D.G. representations of near-rings. Next, we investigate some properties of monogenic R-groups, faithful monogenic R-groups and a generalization of annihilator concepts in R-groups.

• East Asian mathematical journal
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• v.19 no.1
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• pp.151-164
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• 2003

Throughout this paper, we will consider that R is a near-ring and G is an R-group. We initiate the study of monogenic and strongly monogenic R-groups and their basic properties. Also, we investigate some properties of D.G. R-groups, faithful R-groups and monogenic R-groups and we determine that when near-rings are rings.

• East Asian mathematical journal
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• v.17 no.2
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• pp.287-295
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• 2001

• Communications of the Korean Mathematical Society
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• v.19 no.4
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• pp.601-618
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• 2004

Throughout this paper, we will consider that R is a near-ring and G an R-group. We initiate the study of monogenic, strongly monogenic R-groups, 3 types of nonzero R-groups and their basic properties. At first, we investigate some properties of D.G. (R, S)-groups, faithful R-groups, monogenic R-groups, simple and R-simple R-groups. Next, we introduce modular right ideals, t-modular right ideals and 3 types of primitive near-rings. The purpose of this paper is to investigate some properties of primitive types near-rings and their characterizations.