• 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.

• Korean Journal of Mathematics
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• v.16 no.3
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• pp.271-280
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• 2008

In this paper, we initiate a study of faithful R-group G and some substructures of R and G. Next, we investigate a faithful representation of near-ring R and some properties of monogenic Rgroups.

• 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.

• 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.

• 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 applied mathematics & informatics
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• v.30 no.1_2
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• pp.347-352
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• 2012

In this paper, we denote that $R$ is a near-ring and $G$ an $R$-group. We initiate the study of faithful $R$-group, the substructures of $R$ and $G$, also quotients of substructure relations between them. Next, we investigate some isomorphic properties of near-rings and $R$-groups.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.573-583
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• 2005

In this paper, all near-rings R are left near-rings and all representations of R are (right) R-groups. We start with a study of AR, almost AR and AGR rings which are motivated by the works on the Sullivan's Problem [10] and its properties. Next, for any R-group G, we introduce a notion of R-groups with M R-property and investigate their properties and some characterizations of these R-groups. Finally, for the faithful M R-property, we get a commutativity of near-rings and rings.

• Journal of the Korean Mathematical Society
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• v.42 no.6
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• pp.1153-1167
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• 2005

In this paper, all rings and all near-rings R are associative, all modules are right R-modules. For a near-ring R, we consider representations of R as R-groups. We start with a study of AGR rings and their properties. Next, for any right R-module M, we define a new concept GM module and investigate the commutative property of faithful GM modules and some characterizations of GM modules. Similarly, for any near-ring R, we introduce an R-group with MR-property and some properties of MR groups.

• 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.